a boat takes 2 hours to travel 15 miles upstream against the current
. If he can paddle 5 miles upstream in the same amount of time as it takes his to paddle 10 miles downstream, what is the speed of the current? We know that Maria does 1/4 reports 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 Two people working together can complete a job in six hours. Find the speed (mph) of Boriss kayak in still water. First, let us explain the meaning of "upstream" and "downstream.". View this answer View a sample solution Step 1 of 3 Step 2 of 3 Step 3 of 3 Back to top The total time of the trip is 10 hours. Again, it is very important that we check this result. The passenger train travels 440 miles in the same time that the freight train travels 280 miles. Because the speed of the current is 8 miles per hour, the boat travels 150 miles upstream at a net speed of 24 miles per hour. A-258, Bhishma Pitamah Marg, Problem 7. When a boat travels in the same direction as the current, we say that it is traveling downstream. Australia, Leverage Edu Tower, This is reflected in the entries in the second row of Table \(\PageIndex{5}\). Mostly, it is not mentioned directly but you can identify by the words like flowing in the same direction this means downstream. It takes Sanjay 7 hours to paint the same room. So after 5 hours, the distance traveled upstream would be 5(y-x) . Each of these linear equations is easily solved. If the speed of the boat in still water is 10 mph, the speed of the stream is: 2 mph; 2.5 mph; 3 mph ; 4 mph; None of These; Answer: 2 mph . Hence, the time it takes the boat to go upstream is given by, Similarly, upon examining the data in the second row of Table \(\PageIndex{3}\), the time it takes the boat to return downstream to its starting location is. What is the speed of the boat in still water? Emily can paddle her canoe at a speed of 2 mph in still water. It travels 150 miles upstream against the current then returns to the starting location. Our chart now looks like . The sum of the reciprocals of two consecutive integers is \(\frac{19}{90}\). Set this equal to 7/10. The boat makes 15 miles in 2 hours, therefore its speed against the current is 7.5 mph. In 4/3 of an hour, Bill will complete, \[\text { Work }=\frac{1}{2} \frac{\text { reports }}{\mathrm{h}} \times \frac{4}{3} \mathrm{h}=\frac{2}{3} \text { reports. If the current in the river is 3 miles per hour, find the speed of the boat in still water. A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. We want to find two things-- the speed of the boat in
Going upstream, the boat struggles against the current, so its net speed is 32c miles per hour. Find the number(s). our information in it: A boat can travel 16 miles up a river in 2 hours. The total time of the trip is 5 hours. 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 . 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 painter can paint 4 walls per hour. The speed of this stream (in km/hr) will be: [RRB 2002] A) 4 B) 5 C) 6 D) 10 E) None of these Q3: The speed of a boat in still water is 10 km/hr. 1] . This will take 150/40 or 3.75 hours. On your markGet setMental Math Madness! Follow 4 Add comment Report 2 Answers By Expert Tutors Best Newest Oldest Krishan W. answered 02/17/15 Tutor New to Wyzant Leverage Edu Tower, as required by the problem statement. .
Let's say I'm in a 10 mph current in a canoe. Step-by-step solution Chapter 2.2, Problem 85P is solved. 5 May 2016 \[\begin{aligned}\color{blue}{(32-c)(32+c)}\left(\frac{150}{32-c}+\frac{150}{32+c}\right) &=10\color{blue}{(32-c)(32+c)} \\ 150(32+c)+150(32-c) &=10\left(1024-c^{2}\right) \end{aligned}\]. The sum of the reciprocals of the two numbers is 7/10. Answer by josmiceli (19441) ( Show Source ): You can put this solution on YOUR website! Junior's boat will go 15 miles per hour in still water. Expand, simplify, make one side zero, then factor. We know that Bill does 1/2 reports per hour. Or, What is the hardest exam in the world? Here is the guiding principle. | CE Board Problem in Mathematics, Surveying and Transportation Engineering Home Date of Exam: November 2018 Subject: If I can row 2 mph, I can go 12 mph downstream, orrrrrr if I try to go upstream, I'm gonna actually be going backward 8 mph (2 - 10 = -8). by Martynabucytram11, \[\frac{1}{2}+\frac{1}{5}=\frac{5}{10}+\frac{2}{10}=\frac{7}{10}\], However, we found a second value for the first number, namely x = 5/14. What are we trying to find in this problem? Therefore, their combined rate is 1/2 + 1/4 reports per hour. Then the speed of the car is
The third entry in each row is time. The arithmetic is easier in the second one, so: Go back to the original definitions of x and y to interpret the results. Using the relation , distance = speed x time, we get. Example 4. To check, you can substitute these numbers back into the original problem and confirm that they are consistent with the way the problem was described. For Free. Introducing Cram Folders! The trip each way is 150 miles. 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved. How much time will it take to come back? it's moving upstream and downstream on a river. Let x =
Thus, Hank is working at a rate of 1/H kitchens per hour. If they work together, it takes them 3 hours. 2281 . will become 8 = B-C. \[\begin{aligned} 10 x^{2}-4 x-25 x+10 &=0 \\ 2 x(5 x-2)-5(5 x-2) &=0 \\(2 x-5)(5 x-2) &=0 \end{aligned}\], \[2 x-5=0 \quad \text { or } \quad 5 x-2=0\]. It takes Jean 15 hours longer to complete an inventory report than it takes Sanjay. Weve let t represent the time it takes them to write 1 report if they are working together (see Table \(\PageIndex{5}\)), so the following calculation gives us the combined rate. In our discussion above, we pointed out the fact that rates add. The speed of a boat in still water is 15 mi/hr. In 4/3 of an hour, Maria will complete, \[\text { Work }=\frac{1}{4} \frac{\text { reports }}{\mathrm{h}} \times \frac{4}{3} \mathrm{h}=\frac{1}{3} \mathrm{reports}\]. On the other hand, if the boat is traveling downstream, the current will
Required fields are marked *. So we have one equation: 5(y-x) = 100. At last, practice makes the students perfect. The speed of the boat as it goes downstream (with the current) will be 4 miles per hour. You will only be able to solve these questions if you have memorized the boats and streams formula. Example The speed of the boat when traveling downstream is 32 km/hr. Here's what the chart looks like before we put any of
The boat travels downstream 150 miles at a net speed of 40 miles per hour. The speed of a boat in still water is 15 mi/hr. Going downstream, it can travel 60 miles in the same amount of time. A-258, Bhishma Pitamah Marg, Block A, : 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 The boat travels at miles per hour in still water. Her parents names were Marie- Madel Unit 3: Instructor Graded Assignment
Let's see what kinds of equations we can come up with. If Jane can do a certain job in 6 hours, but it takes Ana only 4 hours, how long will it take them if they work together? 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. A little thought reveals that this result is nonsense. Find the speed (mph) of Jacobs canoe in still water. He calculated the speed of the river that day as 1 km/hr. 2003-2023 Chegg Inc. All rights reserved. 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. x15. It takes the same boat 6 hours to travel 12 miles upstream. A woman deposits $600 into an account that pays 5 1/4 interest per year. That is, Maria will complete 1/3 of a report. Thus. . What is the speed of the current? is B+C miles per hour. distance = rate * time UPSTREAM 9 r-3 DOWNSTREAM 11 r+3 Time= distance/rate EQUATION: Time up = Time down She paddles 5 miles upstream against the current and then returns to the starting location. Multiply both sides of this equation by the common denominator 12H(H + 7). Find the speed of the freight train. If they work together, how long will it take them? \[\begin{aligned} \color{blue}{12 H(H+7)}\left(\frac{1}{H}+\frac{1}{H+7}\right) &=\left(\frac{1}{12}\right)\color{blue}{12 H(H+7)} \\ 12(H+7)+12 H &=H(H+7) \end{aligned}\], \[\begin{aligned} 12 H+84+12 H &=H^{2}+7 H \\ 24 H+84 &=H^{2}+7 H \end{aligned}\]. The integer pair {5, 28} has product 140 and sum 23. Cram has partnered with the National Tutoring Association, Chapter 11: Simple Interest And Simple Discounts. It takes you the same amount of time to travel 15 miles downstream, with the current, as 9 miles upstream, against the current. Hence, the sum of x and its reciprocal is represented by the rational expression x + 1/x. Find the speed of the current and the speed of the boat in still water. Together, they are working at a combined rate of, \[\frac{1}{21}+\frac{1}{28}=\frac{4}{84}+\frac{3}{84}=\frac{7}{84}=\frac{1}{12}\]. Without knowing the accurate boats and streams formula it is impossible for any applicant to solve the question. answered 02/17/15, Olubunmi B. Find the two numbers. answered 11/14/20. Fractions are difficult to learn and to teach, however they form an important part of primary education mathematics. Find the two numbers. While returning because of water resistance, it took 1 hour 15 minutes to cover the same distance. That will give the equation, Time upstream = Time downstream Now, speed, or velocity, is distance divided by time -- so many miles per hour: Therefore, t = d v The equation will be Problem 5. That is, if x = 5/2, then its reciprocal is 2/5. Here is a useful piece of advice regarding distance, speed, and time tables. Then the speed of boat in still water and the speed of current are respectively. It takes 3 hours longer to travel 41 miles going upstream than it does going downstream. What is the speed of the current? Signature Assignment for EDEL 462 The speed of the boat as it goes downstream (with the current) will be 4 miles per hour. Find the two numbers. Is it something that matters in the preparation for competitive exams? Stream- The water that is moving in the river is called a stream. It can go 24 mile downstream with the current in the same amount of time. \[Rate \(=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { report }}{2 \mathrm{h}}\)\]. Consequently, if the first number is x = 2, then the second number is 2x + 1, or 2(2) + 1. For example, in the first row, d = 60 miles and v = 3 c miles per hour. Moira can paddle her kayak at a speed of 2 mph in still water. How do we find the two equations we need? in the chart for the time downstream. at a rate of B miles per hour. Most questions answered within 4 hours. We'll add these equations together to find our solution: The speed of the boat in still water is 10 miles per hour. The boat travels at miles per hour in still water. To see the equation, pass your mouse over the colored area. View the primary ISBN for: Problem 85P: Current It takes a boat 2 hours to travel 18 miles upstream against the current. 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. Find the rate of the current and the rate of the boat in still water. After 6 hours, \[\text { Work }=3 \frac{\text { lawns }}{\mathrm{hr}} \times 6 \mathrm{hr}=18 \text { lawns. Our team will review it before it's shown to our readers. Freshwater, Sydney, NSW 2096, Answer: 1 hour 15 minutes. To find the speed of the current, we can substitute 10
That is, together they work at a rate of 1/t reports per hour. The return trip takes2. hours going downstream. On the return trip, the boat benefits from the current, so its net speed on the return trip is 32 + c miles per hour. In a river with unknown current, it takes the boat twice as long to travel 60 miles upstream (against the current) than it takes for the 60 mile return trip (with the current). Australia, Meet 75+ universities in Mumbai on 30th April, What is an idiom? If we divide both sides of the second equation by 3,
Q2: The motorboat whose speed is 15 km/hr in still water, will go 30 km downstream and come back in a total of 4 hours 30 minutes. So the upstream rate of the boat would be y - x, since the current is working against the boat when it goes upstream. If they work together, it takes them 12 hours. Raymond can do a job in 3 hours, while it takes Robert 2 hours. Clearly, working together, Bill and Maria will complete 2/3 + 1/3 reports, that is, one full report. For example, suppose that Emilia can mow lawns at a rate of 3 lawns per hour. An OTP has been sent to your registered mobile no. Defence Colony, New Delhi, How long will it take them if they work together? The sum of the reciprocals of two consecutive integers is \(\frac{19}{90}\). the speed of the boat in still water? If the second number is 1 larger than twice the first number, then the second number can be represented by the expression 2x + 1. Accessibility StatementFor more information contact us [email protected] check out our status page at https://status.libretexts.org. United Kingdom, EC1M 7AD, Leverage Edu So, your trip will take 50 minutes from your dock to the island. Solution. The rate of the current is 15 km/hour and the . \[\frac{1}{x}+\frac{1}{2 x+1}=\frac{7}{10}\]. 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 \(\PageIndex{5}\). If the boat is traveling
What is the speed (in mph) of the current? To cover the answer again, click "Refresh" ("Reload").But do the problem yourself first! The sum of a number and its reciprocal is \(\frac{41}{20}\). 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. That is, Bill will complete 2/3 of a report. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Because it takes Liya 7 more hours than it takes Hank, let H + 7 represent the time it takes Liya to paint the kitchen when she works alone. 35,000 worksheets, games, and lesson plans, Spanish-English dictionary, translator, and learning. a. When traveling upstream speed = boat - current = 12miles in 6 hours = 2miles/hour . Find the speed of the current. Let's use the same logic going downstream. In downstream it takes 3 hours to travel 36 km. Problem 12. Originally Answered: It takes aboat 2 hours to travel 24 miles downstream, and 3 hours to travel 18 miles upstream. It will . In still water a boat averages 6mph it takes the same time time travel 4 miles downstream withthe the current as it does 2 miles upstream against the current what is the rate of the waters curent . Thus, Bill is working at a rate of 1/2 report per hour. Downstream- When the boat is flowing in the same direction as the stream, it is called Downstream. This will take 150/24 or 6.25 hours. 3.17.8: Applications of Rational Functions is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts. If we let c represent the speed of the current in the river, then the boats speed upstream (against the current) is 3 c, while the boats speed downstream (with the current) is 3 + c. Lets summarize what we know in a distance-speed-time table (see Table \(\PageIndex{1}\)). If the rate of the boat in still water is 13 miles per hour what is the rate of the - 20218675 Multiply both sides of this equation by the common denominator 10x(2x + 1). Current It takes a boat 2 hours to travel 18 miles upstream against the current. We know that if the boat were on a still lake, its motor would propel it
Most questions answered within 4 hours. The passenger train travels 518 miles in the same time that the freight train travels 406 miles. This result is also recorded in Table \(\PageIndex{6}\). The same boat can travel 36 miles downstream in 3 hours. If one of them works twice as fast as the other, how long would it take the faster one working alone? We'll put 16 in our chart for the distance upstream, and we'll put 2 in
Using the equation speed = distance/time: 12 miles upstream take 1.5 hours, so v-w=12/1.5=24/3=8 m/h, 24 miles downstream take 1.5 hours as well, so v+w=24/1.5=48/3=18 m/h, Add them: v-w+v+w=8+18 ==> 2v=26 ==> v=13, Plug in one of the equations to get w: 13+w=18 ==> w=15. Lesson Plan Making educational experiences better for everyone. We weren't able to detect the audio language on your flashcards. A common misconception is that the times add in this case. A motorboat 5 hours to travel 100km upstream. The sum of the reciprocals of two consecutive even integers is \(\frac{11}{60}\). A boat takes 2 hours to travel 15 miles upriver against the current. Solution. A boat travels at a constant speed of 3 miles per hour in still water. \[\begin{array}{l}{0=H^{2}+7 H-24 H-84} \\ {0=H^{2}-17 H-84}\end{array}\]. Then. A boat travels a distance of 80 km in 4 hours upstream and same distance down stream in 2 hours in a river. Uttar Pradesh 201301, Devonshire House, 60 Goswell Road, Let x be the distance to Boston. Their reciprocals, respectively, are 1/x and 1/(2x + 1). Mr. Larlham A boat can travel 12 miles upstream in the same amount of time it takes to travel 18 miles downstream. What was the interest rate on the loan? No packages or subscriptions, pay only for the time you need. it will become 12 = B+C. 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. If they work together, it takes them 8 hours. Best Answer #1 +118288 +10 . The sum of a number and twice its reciprocal is \(\frac{9}{2}\). Break up the middle term of the quadratic trinomial using this pair, then factor by grouping. Denote the speed of the boat by v and the speed of the current by w. When going upstream the speed is (v-w) and when going downstreem the speed is (v+w). The speed of the boat in still water is 3 miles per hour. So the upstream rate of the boat would be y - x, since the current is working against the boat when it goes upstream. Note how weve entered this result in the first row of Table 6. If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? The sum of the reciprocals of two consecutive odd integers is \(\frac{16}{63}\). Angie Gunawardana The reciprocals are 14/5 and 7/2, and their sum is, \[-\frac{14}{5}+\frac{7}{2}=-\frac{28}{10}+\frac{35}{10}=\frac{7}{10}\]. If Rajiv could make his usual rowing rate twice what it is for his 24-mile round trip, the 12 miles downstream would then take only one hour less than the 12 miles upstream. \[\begin{aligned} \color{blue}{10 x}\left(x+\frac{1}{x}\right) &=\left(\frac{29}{10}\right) \color{blue}{10 x}\\ 10 x^{2}+10 &=29 x \end{aligned}\]. We have advice similar to that given for distance, speed, and time tables. Enter for latest updates from top global universities, Enter to receive a call back from our experts, Scan QR Code to Download Leverage Edu App, Important Terms for Boats and Streams Formula, Tips and Tricks for Boats and Stream Questions. How many hours will it take if they work together? Therefore, The rate of current is, Hence, The required rate of current is 1.6. We eliminate the solution H = 4 from consideration (it doesnt take Hank negative time to paint the kitchen), so we conclude that it takes Hank 21 hours to paint the kitchen. If 180 cubic centimeters of water is frozen, by how many cubic centimeters will its volume increase? A boat takes 2 hours to travel 15 miles upriver against the current. How long does it take Hank to complete the job if he works alone? Please make a donation to keep TheMathPage online.Even $1 will help. 5600 = ___________________ It takes the same time for the boat to travel 5 miles upstream as it does to travel 10 miles downstream. Rate problems are based on the relationship Distance
= (Rate)(Time). We can make the numbers a bit smaller by noting that both sides of the last equation are divisible by 10. How long will it take them to finish the report if they work together? How many hours would it take Amelie if she worked alone? Really? Lets look at some applications that involve the reciprocals of numbers. So now we have a second equation: 2(y+x) = 100. Please verify. How many hours would it take Sanjay if he worked alone? When traveling downstream speed = boat + current = 20miles in 2 hours = 10miles/hour. Expand and simplify each side of this result. Thus, our two numbers are x and 2x+1. Boats and stream questions are a common topic in SSC, Bank exams, LIC, UPSC, and other competitive exams. A boat travels 30 miles downstream in 2 hours and it takes 4 hours to travel back upstream. We start by recalling the definition of the reciprocal of a number. Dont let it confuse you. we need to write our two equations. Mark M. In similar fashion, the time to travel downstream is calculated with. Hence, the speed of the current is 1 mile per hour. Find the number(s). Lesson Title: A boat takes 2 hours to travel 15 miles upriver against the current. What is the rate of the boat in still water and what is the rate of the current? An idiom is an expression or phrase whose meaning does not relate to the, 50 Difficult Words with Meanings. The total time of the trip is 9 hours. For any nonzero real number a, the reciprocal of a is the number 1/a. Together, they can complete the same job in 12 hours. If Rajiv rows at his usual rate, he can travel 12 miles downstream in a . What is the speed of the current of the river? It takes Hank 21 hours to complete the kitchen, so he is finishing 1/21 of the kitchen per hour. It takes Sanjay 9 hours to paint the same room. Find the rate of the current and the rate of the boat in still water. It takes Liya 7 more hours to paint a kitchen than it takes Hank to complete the same job. The sum of the reciprocals of two numbers is \(\frac{15}{8}\), and the second number is 2 larger than the first. How many hours will it take if they work together? How long does it take him to go 5 km in stationary water? Let x represent the first number. be pushing the boat faster, and the boat's speed will increase by C miles
However, as we saw above, the rates at which they are working will add. Katrina drove her car to Boston at a speed of 100 kph (kilometers per hour). He started at the tower's base and is now 35 feet above the ground. for the B in any of our equations. which is 100 km. Maria can finish the same report in 4 hours. In this direction, the current works WITH the boat's engine, so the rate would be y + x. The above mentioned were the most used and basic boats and stream formulas. The reciprocal of x is 1/x. Save my name, email, and website in this browser for the next time I comment. 1] . How long it takes the faster one. Multiply both sides of this equation by the common denominator 4t. Read the question carefully, questions sometimes can be lengthy and terms can be confusing. Most questions answered within 4 hours. 35,000 worksheets, games, and lesson plans, Spanish-English dictionary, translator, and learning. { "3.17.01:_Introducing_Rational_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.
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