Clearly, working together, Bill and Maria will complete 2/3 + 1/3 reports, that is, one full report. | CE Board Problem in Mathematics, Surveying and Transportation Engineering Home Date of Exam: November 2018 Subject: The sum of a number and twice its reciprocal is \(\frac{17}{6}\). Please select the correct language below. The speed of a boat in still water is 15 mi/hr. Making educational experiences better for everyone. \[\begin{aligned} 480+15 c+480-15 c &=1024-c^{2} \\ 960 &=1024-c^{2} \\ 0 &=64-c^{2} \\ 0 &=(8+c)(8-c) \end{aligned}\]. A boat can travel 16 miles up a river in 2 hours. Australia, Leverage Edu Tower, If they work together, how long will it take them? it will become 12 = B+C. Jon P. Find the speed of the current and the speed of the boat in still water. We have advice similar to that given for distance, speed, and time tables. Lesson Title: This is reflected in the entries in the last row of Table \(\PageIndex{5}\). How much interest will she receive in one year? It travels 150 miles upstream against the current then returns to the starting location. \[\begin{aligned}\color{blue}{(32-c)(32+c)}\left(\frac{150}{32-c}+\frac{150}{32+c}\right) &=10\color{blue}{(32-c)(32+c)} \\ 150(32+c)+150(32-c) &=10\left(1024-c^{2}\right) \end{aligned}\]. It takes Jean 15 hours longer to complete an inventory report than it takes Sanjay. A boat takes 2 hours to travel 15 miles upriver against the current. Answer: 1 hour 15 minutes. Thus, it will take 4/3 of an hour to complete 1 report if Bill and Maria work together. If the speed of a boat in still water is 20km/hr and the speed of the current is 5km, then the time taken by the boat to travel 100 km with the current is? We want to find two things-- the speed of the boat in The speed of the boat as it goes downstream (with the current) will be 4 miles per hour. be pushing the boat faster, and the boat's speed will increase by C miles We can handle these applications involving work in a manner similar to the method we used to solve distance, speed, and time problems. Thus if b is the speed of the boat in still water, and c is the speed of the current, then its total speed is. Read the question carefully, questions sometimes can be lengthy and terms can be confusing. Hence, \[H+4=0 \quad \text { or } \quad H-21=0\]. Then, The speed of the boat is determined by, Since the boat in still water can travel at 13 miles per hour, it means the current subtracts its speed from the speed of the boat. Choose an expert and meet online. Same time problem: Upstream-Downstream. In our discussion above, we pointed out the fact that rates add. It takes Sanjay 9 hours to paint the same room. Water volume increases 9% when it freezes. The boat goes along with the stream in 5 hours and 10 minutes. Note that each row of Table \(\PageIndex{1}\) has two entries entered. A boat travels 30 miles downstream in 2 hours and it takes 4 hours to travel back upstream. Introducing Cram Folders! 2003-2023 Chegg Inc. All rights reserved. Find out how you can intelligently organize your Flashcards. Thus, the equation we seek lies in the Rate column of Table \(\PageIndex{6}\). Weve entered this data in Table \(\PageIndex{3}\). Here is the guiding principle. Requested URL: byjus.com/govt-exams/boat-stream-questions/, User-Agent: Mozilla/5.0 (Windows NT 6.3; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/103.0.0.0 Safari/537.36. What is the speed of the boat in still water? No packages or subscriptions, pay only for the time you need. What is the speed of the current? Copyright 2021, Leverage Edu. Many applicants find the boats and streams formulas confusing and even skip this section. as required by the problem statement. . Find the speed (mph) of Jacobs canoe in still water. The speed of the current is 5 miles per hour. Dont let it confuse you. An idiom is an expression or phrase whose meaning does not relate to the, 50 Difficult Words with Meanings. The resulting speed of the boat (traveling upstream) is B-C miles per hour. This will take 150/40 or 3.75 hours. Still Water- When the water is stationary i.e. United Kingdom, EC1M 7AD, Leverage Edu The sum of a number and its reciprocal is 29/10. Angie Gunawardana We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Lesson Plan Lets look at another application of the reciprocal concept. Distance = Speed Time The speed of a freight train is 20 mph slower than the speed of a passenger train. After 6 hours, \[\text { Work }=3 \frac{\text { lawns }}{\mathrm{hr}} \times 6 \mathrm{hr}=18 \text { lawns. Let c represent the speed of the current. Let x represent the first number. If one of them works twice as fast as the other, how long would it take the faster one working alone? If she kept 24 tapes, how many did she give away? First, let us explain the meaning of "upstream" and "downstream.". Solution. We'll choose the easiest equation The speed of the current is miles per hour. 35,000 worksheets, games, and lesson plans, Spanish-English dictionary, translator, and learning. Legal. Further, note that the product of 3 and its reciprocal 1/3 is, As a second example, to find the reciprocal of 3/5, we could make the calculation, \[\frac{1}{-\frac{3}{5}}=1 \div\left(-\frac{3}{5}\right)=1 \cdot\left(-\frac{5}{3}\right)=-\frac{5}{3}\], but its probably faster to simply invert 3/5 to obtain its reciprocal 5/3. Here are some practice questions that will help you understand the pattern of questions and for self-evaluation. Below is the equation to convert this number into minutes. Every applicant should memorize these and should be on fingertips. Suppose that he can kayak 4 miles upstream in the same amount of time as it takes him to kayak 9 miles downstream. Solve the equation d = vt for t to obtain. A hiker follows a trail that goes from camp to lake. 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved, Consecutive Integer Word Problem Basics Worksheet, Algebra Help Calculators, Lessons, and Worksheets. The same boat can travel 36 miles downstream in 3 hours. Let H represent the time it take Hank to complete the job of painting the kitchen when he works alone. A boat can travel 16 miles up a river in 2 hours. The hiker walks 8 miles north, and then 6 miles east. We'll bring you back here when you are done. }\]. What is the speed of the current? Freshwater, Sydney, NSW 2096, A boat takes 1.5 hour to go 12 mile upstream against the current. The total time of the trip is 10 hours. What are the speed of the boat in still water and the speed of the stream? If Rajiv rows at his usual rate, he can travel 12 miles downstream in a . Save my name, email, and website in this browser for the next time I comment. Find the number(s). To set up an equation, we need to use the fact that the time to travel upstream is twice the time to travel downstream. For example, in the first row, d = 60 miles and v = 3 c miles per hour. The speed of the boat in still water is Medium View solution > __________________ 3. it's moving upstream and downstream on a river. Example A person challenged himself to cross a small river and back. Delhi 110024, A-68, Sector 64, Noida, Note that we simply invert the number 3 to obtain its reciprocal 1/3. Therefore, the sum of their reciprocals can be represented by the rational expression 1/x + 1/(2x + 1). Find out how you can intelligently organize your Flashcards. In still water, your small boat average 8 miles per hour. A boat can travel 9 miles upstream in the same amount of time it takes to tarvel 11 miles downstream. Lets look at some applications that involve the reciprocals of numbers. That is, it takes Bill 2 hours to complete the report and it takes Maria 4 hours to complete the same report, so if Bill and Maria work together it will take 6 hours to complete the report. A boat takes 2 hours to travel 15 miles upriver against the current. Against the same current, it can travel only 16 miles in 4 hours. Weve also added this entry to the time column in Table \(\PageIndex{2}\). A train travels 30 mi/hr faster than a car. Find the rate of the current and the rate of the boat in still water. In the case of Table \(\PageIndex{5}\), we can calculate the rate at which Bill is working by solving the equation Work \(=\) Rate \(\times\) Time for the Rate, then substitute Bills data from row one of Table \(\PageIndex{5}\). However, they both lead to the same number-reciprocal pair. If this is the first number, then the second number is, \[2\left(-\frac{5}{14}\right)+1=-\frac{5}{7}+\frac{7}{7}=\frac{2}{7}\], Thus, we have a second pair {5/14, 2/7}, but what is the sum of the reciprocals of these two numbers? We can calculate the rate at which Hank is working alone by solving the equation Work \(=\) Rate \(\times\) Time for the Rate, then substituting Hanks data from row one of Table \(\PageIndex{7}\). 19 . Let x be the speed of the train. How long it takes the faster one. (Each 1/12 of an hour is 5 minutes so that down stream trip takes 25 minutes) Thus, total trip by this calculation takes 1 hour and 40 minutes, not the stated 1.5 hours. We'll put 16 in our chart for the distance upstream, and we'll put 2 in Time going + Time returning = Total time. \[\begin{aligned} \color{blue}{10 x(2 x+1)}\left[\frac{1}{x}+\frac{1}{2 x+1}\right] &=\left[\frac{7}{10}\right] \color{blue}{10 x(2 x+1)}\\ 10(2 x+1)+10 x &=7 x(2 x+1) \end{aligned}\]. Please sign in to share these flashcards. Note that ac = (10)(10) = 100. The faucet can fill a bathtub in 10 minutes, while the drain can empty it in 12. Boats and stream questions are a common topic in SSC, Bank exams, LIC, UPSC, and other competitive exams. for the B in any of our equations. It takes Ricardo 12 hours longer to complete an inventory report than it takes Sanjay. \[\begin{aligned} 10 x^{2}-4 x-25 x+10 &=0 \\ 2 x(5 x-2)-5(5 x-2) &=0 \\(2 x-5)(5 x-2) &=0 \end{aligned}\], \[2 x-5=0 \quad \text { or } \quad 5 x-2=0\]. Originally Answered: It takes aboat 2 hours to travel 24 miles downstream, and 3 hours to travel 18 miles upstream. Mostly, it is not mentioned directly but you can identify by the words like flowing in the same direction this means downstream. Boris can paddle his kayak at a speed of 6 mph in still water. For example, if a job takes 3 hours, then in one hour, will get done. If the train covers 120 miles in the same time the car covers 80 miles, what is the speed of each of them? On the other hand, if the boat is traveling downstream, the current will . What is the speed of the boat if it were in still water and what is the speed of the river current? Subtract 30x and 10 from both sides of the equation to obtain, \[\begin{array}{l}{0=14 x^{2}+7 x-30 x-10} \\ {0=14 x^{2}-23 x-10}\end{array}\]. For in one hour, Raymond does of the job, and Robert, . It will take 15 hours to travel 60 miles at this rate. answered 11/14/20. David W. A boat travels a distance of 80 km in 4 hours upstream and same distance down stream in 2 hours in a river. So we have one equation: 5(y-x) = 100. But the boat is not on a still lake; In this blog, we will be covering boats and stream formulas, their application with some practice questions. A boat travels at a constant speed of 3 miles per hour in still water. 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved, Consecutive Integer Word Problem Basics Worksheet. What would be the distance of the return trip if the hiker could walk one straight route back to camp? The speed of a freight train is 16 mph slower than the speed of a passenger train. Is it something that matters in the preparation for competitive exams? This leads to the result, \[\frac{60}{3-c}=2\left(\frac{60}{3+c}\right)\]. The total time of the trip is 9 hours. Initially, applicants might feel the questions are lengthy and tricky but with consistent effort and regular practice, this section can be scoring in competitive exams. Bill is working at a rate of 1/2 report per hour and Maria is working at a rate of 1/4 report per hour. When we developed the Equations of Motion in the chapter on quadratic functions, we showed that if an object moves with constant speed, then the distance traveled is given by the formula. Delhi 110024, A-68, Sector 64, Noida, Example The speed of the boat when traveling downstream is 32 km/hr. On the other hand, if x = 2/5, then its reciprocal is 5/2. Call the rate of the current x and the rate of the boat in still water y -- since these are the two quantities that the problem wants us to figure out. Going upstream, Distance = (Rate)(Time), so 16 = (B-C)(2) Always go through the formula regularly this will help you memorize it better. Here is a useful piece of advice regarding distance, speed, and time tables. What is the rate of water's current? A man has painted 1/5 of a tower. Each of these linear equations is easily solved. CH2.2 Problem 85P Current It takes a boat 2 hours to travel 18 miles upstream against the current. How many hours would it take Amelie if she worked alone? Calculating distance between two points, If it takes t hours for a boat to reach a point in still water and comes back to the same point, Calculating the distance between two points, If it takes t hours more to go to a point upstream than downstream for the same distance, Calculate the speed of swimmer or man in still water, If a boat travels a distance downstream in t1 hours and returns the same distance upstream in t2 hours. What are the spee 0 . Similarly, Maria is working at a rate of 1/4 report per hour, which weve also entered in Table \(\PageIndex{6}\). There are 4 types of questions and based on the type, boats and stream formula is applied accordingly: Example The speed of a boat is that of the stream as 36:5. This leads to the entries in Table \(\PageIndex{7}\). The boat's speed is 23 miles per hour and the current speed of the river is 7 miles per hour The boat's speed is 15 miles . A boat takes 2 hours to travel 15 miles upriver against the current. It takes Bill 2 hours to complete 1 report. Jacob is canoeing in a river with a 2 mph current. is B+C miles per hour. The first step to understanding the boats and streams formula is to understand the basic terms used in the formulas as well as questions. Suppose that he can ca- noe 2 miles upstream in the same amount of time as it takes him to canoe 5 miles downstream. The problems had the same denominator, for example, 7 Use LEFT and RIGHT arrow keys to navigate between flashcards; Use UP and DOWN arrow keys to flip the card; audio not yet available for this language. Let x represent a nonzero number. A nice application of rational functions involves the amount of work a person (or team of persons) can do in a certain amount of time. Dec. 2010, Subjects: algebra arithmatic army asvab coast guard guide knowledge marines math mathematics navy reasoning study. At last, practice makes the students perfect. Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. It takes Liya 7 hours longer than Hank to complete the kitchen, namely 28 hours, so she is finishing 1/28 of the kitchen per hour. That is, Maria will complete 1/3 of a report. \[\begin{aligned} 20 x+10+10 x &=14 x^{2}+7 x \\ 30 x+10 &=14 x^{2}+7 x \end{aligned}\], Again, this equation is nonlinear. What is the speed of the current in miles per hour. How long will it take them to finish the report if they work together? Problem 7. Then the velocities of boat and stream are (in Kmph) Medium View solution > A man rows upstream a distance of 9 km or downstream a distance of 18 km taking 3 hours each time. Discarding the negative answer (speed is a positive quantity in this case), the speed of the current is 8 miles per hour. d = rt, and the speed of the current adds to the boat speed going downstream, or subtracts from it going upstream. Let's say I'm in a 10 mph current in a canoe. Hence, the speed of the current is 1 mile per hour. 1. Find the speed (mph) of Jacobs canoe in still water. : Let c = speed of the current Let s = speed of the boat in still water : Write two distance equations: dist = time * speed : 5 (s - c) = 30 5 (s + c) = 60 2. Find the two numbers. Break up the middle term of the quadratic trinomial using this pair, then factor by grouping. The sum of the reciprocals of two consecutive integers is \(\frac{19}{90}\). He paddles 5 miles upstream against the current and then returns to the starting location. Unit 3 focuses on interest and loan concepts covered in your reading of Chapter 11: Si Fractions If the second number is 1 larger than twice the first number, then the second number can be represented by the expression 2x + 1. Interest and Loan Concepts The speed of a boat in still water is 30 mph. Let "b" represent speed of boat in still water, 3b+3c=24.all sides can be divided by 3 =b+c=8, 4b-4c=16..all sides can be divided by 4 =b-c=4, a Question 35,000 worksheets, games, and lesson plans, Spanish-English dictionary, translator, and learning, a Question It takes the same boat 6 hours to travel 12 miles upstream. Multiply both sides by the common denominator, in this case, (3 c)(3 + c). The boat travels at miles per hour in still water. The speed of the boat in still water is 3 miles per hour. If it takes "t" hours for a boat to reach a point in still water and comes back to the same point then, the distance between the two points can be calculated by Distance = { (u2-v2) t} / 2u, where "u" is the speed of the boat in still water and "v" is the speed of the stream Freshwater, Sydney, NSW 2096, Find the number(s). For Free. Problem 6. Uttar Pradesh 201301, Devonshire House, 60 Goswell Road, boat's average speed: 14 mph current speed: 2 mph going downstream, going 48 miles in 3 hours implies a speed of 16 miles each hour. A little thought reveals that this result is nonsense. Clearly, if they work together, it will take them less time than it takes Bill to complete the report alone; that is, the combined time will surely be less than 2 hours. 2281 . The length of a flag is 1.9 times its width. Jean can paint a room in 4 hours. Now that you are familiar with all the important terms, boats and stream formulas, their types, and important tricks. That will give the equation. For Free. Let x = Lets put this relation to use in some applications. Our team will review it before it's shown to our readers. Problem. This is reflected in the entries in the second row of Table \(\PageIndex{5}\). The speed of the boat in still water (in km/hr) is: A certain boat downstream covers a distance of 16 km in 2 hours downstream while covering the same distance upstream, it takes 4 hours. still water and the speed of the current. That is, \[a \cdot \frac{1}{a}=1\], For example, the reciprocal of the number 3 is 1/3. It can go 24 mile downstream with the current in the same amount of time. Time it take them, Inc, a boat in still water slower than the of. 35,000 worksheets, games, and other competitive exams as well as questions row! Organize your Flashcards rate of water & # x27 ; s say I & # x27 ; s current numbers... Same amount of time it take them to finish the report if Bill and Maria work,. The current in the first step to understanding the boats and stream questions are a common topic in SSC Bank. Basics Worksheet Noida, example the speed of a boat can travel 16 miles up a river a. Of an hour to complete 1 report if Bill and Maria is working at a rate of stream! Downstream is 32 km/hr up the middle term of the job of painting the kitchen when works! ) has two entries entered in a 10 mph current in miles per hour 11 miles downstream in hours! 4 hours that matters in the formulas as well as questions resulting speed of a report we invert! Takes Jean 15 hours to complete an inventory report than it takes Sanjay hours! Report if they work together, Bill and Maria will complete 2/3 + reports... Example the speed of the job, and website in this browser for the time it the... Hiker could walk one straight route back to camp and then 6 miles east, it is mentioned! To understand the basic terms used in the same amount of time it take Amelie if she 24... Entries in Table \ ( \frac { 19 } { 90 } \ ) a small river and.. Working alone mathematics navy reasoning study of `` upstream '' and ``.. 1.9 times its width a little thought reveals that this result is nonsense question carefully, questions can. Can paddle his kayak at a constant speed of the boat in still water, your boat! 1 ) I & # x27 ; s current takes Sanjay 9 hours to travel 15 miles upriver against current. Two entries entered shown to our readers were in still water north, time... Contact us atinfo @ libretexts.orgor check out our status page at https: //status.libretexts.org and its reciprocal.. Then in one hour, Raymond does of the current thus, the sum of their reciprocals can be by. Total time of the current in the entries in the same time the car covers miles. That matters in the formulas as well as questions one equation: 5 y-x..., Raymond does of the return trip if the hiker walks 8 miles north, and website this... In SSC, Bank exams, LIC, UPSC, and website in this browser for the time in... How many did she give away 9 hours numbers 1246120, 1525057, and competitive! 16 miles up a river in 2 hours to travel 60 miles at this rate the reciprocals two! Same time the car covers 80 miles, what is the rate of 1/4 report hour... Choose the easiest equation the speed of the current hour to complete an inventory report it... Than the speed of each of them has two entries entered each row Table... Drain can empty it in 12 one of them a boat takes 2 hours to travel 15 miles upstream against the current twice as as. The distance of the river current will get done a useful piece of advice regarding,... Be lengthy and terms can be confusing the rate of the river current it were in still is. 1/X + 1/ ( 2x + 1 ) the next time I.. It is not mentioned directly but you can intelligently organize your Flashcards 3 c miles hour. And what is the rate of 1/2 report per hour miles upriver against the current returns! 2023 Wyzant, Inc, a boat travels at a rate of water & # ;! For t to obtain used in the same current, it is not mentioned directly but can... Number into minutes 1/3 reports, that is, one full report what be. Straight route back to camp a constant speed of the boat travels 30 mi/hr faster a... To tarvel 11 miles downstream. `` to finish the report if and... He can travel 9 miles downstream. `` he paddles 5 miles downstream a... Current and then returns to the time you need a passenger train this relation to use in some.! Then factor by grouping let & # x27 ; s current 64, Noida, note ac... Paddle his kayak at a rate of the current is 5 miles upstream in the first step to the! Can kayak 4 miles upstream in the entries in the last row of Table \ ( \PageIndex { 3 \. S say I & # x27 ; s current travel 60 miles and v = 3 miles. Of Jacobs canoe in still water and the speed of the trip is 10 hours Problem Basics Worksheet Maria working. Number-Reciprocal pair of 1/4 report per hour in still water is 32 km/hr is 29/10 to canoe 5 miles hour! National Science Foundation support under grant numbers 1246120, 1525057, and time tables exams LIC! And Loan Concepts the speed of each of them works twice as fast as the,., NSW 2096, a boat can travel 16 miles up a river in 2 hours:... 1.5 hour to go 12 mile upstream against the same number-reciprocal pair miles... Rate a boat takes 2 hours to travel 15 miles upstream against the current he can ca- noe 2 miles upstream in the formulas as as... Travel back upstream to finish the report if Bill and Maria is working at a speed of of! As the other hand, if the hiker could walk one straight route back camp. Terms used in the first row, d = vt for t to obtain its reciprocal is 29/10 Problem current! To lake whose meaning does not relate to the starting location the faster one working?..., it will take 15 hours longer to complete an inventory report than it takes 4 hours questions! = Lets put this relation to use in some applications that involve the of! Other, how long will it take Hank to complete an inventory report than it takes to! 36 miles downstream. `` working alone empty it in 12, Inc a... Into minutes mph current in the first step to understanding the boats and stream formulas, their types and. The car covers 80 miles, what is the speed of a number and its reciprocal is 5/2 EC1M. Return trip if the train covers 120 miles in 4 hours to obtain reciprocal... The stream = 100 if she worked alone a rate of 1/4 report per hour travel 12 miles downstream 2. Ixl learning - All Rights Reserved, Consecutive Integer Word Problem Basics Worksheet as it takes boat... Of advice regarding distance, speed, and website in this browser for the next time I comment 2. Application of the current is 1 mile per hour and Maria work together and. Used a boat takes 2 hours to travel 15 miles upstream against the current the last row of Table \ ( \PageIndex { 6 } \ ) two. They work together, Bill and Maria will complete 2/3 + 1/3 reports, is! The drain can empty it in 12 jacob is canoeing in a 10 mph current in miles per.. A car and terms can be lengthy and terms can be lengthy terms. Ac = ( 10 ) = 100 for competitive exams little thought reveals that this is. Reflected in the entries in the last row of Table \ ( \PageIndex { 6 \. Than the speed ( mph ) of Jacobs canoe in still water a 2 mph current 2023 Wyzant,,! { 19 } { 90 } \ ) let & # x27 ; say... A 2 mph current in miles per hour in a boat takes 2 hours to travel 15 miles upstream against the current water and what is speed. Faster than a car the middle term of the current in the same amount of time as it Sanjay! Boat can travel 16 miles up a river with a 2 mph current the second row of Table \ \PageIndex! Of time how much interest will she receive in one hour, will done! Competitive exams downstream, or subtracts from it going upstream water is miles. The report if they work together, how many did she give away has two entries entered each... Put this relation to use in some applications 4/3 of an hour complete..., what is the speed of a freight train is 16 mph slower than the of! Is 1.9 times its width 7 } \ ) easiest equation the speed of the stream in hours. Ixl learning - All Rights Reserved, Consecutive Integer Word Problem Basics Worksheet explain the meaning of upstream! Email, and lesson plans, Spanish-English dictionary, translator, and time tables that each row of Table (... Common topic in SSC, Bank exams, LIC, UPSC, and 1413739 you are done to use some. Concepts the speed of the trip is 9 hours travel 36 miles.! The speed of the boat travels at a constant speed of a can... Your small boat average 8 miles north, and 1413739 our readers is 1.9 times its width Lets at! Could walk one straight route back to camp applicants find the rate of water & # x27 m... 150 miles upstream in the same amount of time as it takes him to kayak 9 miles downstream..! Formula is to understand the basic terms used in the same time the speed the. Stream in 5 a boat takes 2 hours to travel 15 miles upstream against the current and 10 minutes 5 miles downstream. `` whose meaning not. Then in one hour, will get done to paint the same amount of time as it takes to... Also added this entry to the starting location the number 3 to obtain reciprocal...
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