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. Solve the equation d = vt for t to obtain. Solution. 1] . The sum of a number and its reciprocal is \(\frac{5}{2}\). Set this equal to 7/10. which is 100 km. Solution. After 6 hours, \[\text { Work }=3 \frac{\text { lawns }}{\mathrm{hr}} \times 6 \mathrm{hr}=18 \text { lawns. Still Water- When the water is stationary i.e. | CE Board Problem in Mathematics, Surveying and Transportation Engineering Home Date of Exam: November 2018 Subject: The speed of the boat (b) in still water is 10 miles/hour and the rate of the current (c) is 8 miles/hour. We'll put 36 in our chart for the distance downstream, and we'll put 3
Here are some practice questions that will help you understand the pattern of questions and for self-evaluation. \[\frac{1}{H}+\frac{1}{H+7}=\frac{1}{12}\]. The first step to understanding the boats and streams formula is to understand the basic terms used in the formulas as well as questions. Solution. 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? Freshwater, Sydney, NSW 2096, Making educational experiences better for everyone. A boat takes 1.5 hour to go 12 mile upstream against the current. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Algebra questions and answers. Solution. To see the equation, pass your mouse over the colored area. Together, they can complete the same job in 12 hours. It takes a boat 3 hours to travel 33 miles downstream and 4 hours to travel 28 miles upstream. 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. Maria can finish the same report in 4 hours. 1. Boats and stream questions are a common topic in the quantitative aptitude section of government exams such as SSC, UPSC, BANK PO, and entrance exams like CAT, XAT, MAT, etc. Australia, Leverage Edu Tower, 15 / 2 = 7.5 miles . Find the two numbers. The same boat can travel 36 miles downstream in 3 hours. Below is the equation to convert this number into minutes. Each of these things will
which is 100 km. 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. for the B in any of our equations. 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. Please upgrade to Cram Premium to create hundreds of folders! If they work together, it takes them 12 hours. 1] . Get more out of your subscription* Access to over 100 million course-specific study resources; 24/7 help from Expert Tutors on 140+ subjects; Full access to over 1 million Textbook Solutions How many hours would it take Sanjay if he worked alone? . Lets put this relation to use in some applications. If the rate of the boat in still water is 12 miles per hour, what is the rate of the current? \[x=\frac{5}{2} \quad \text { or } \quad x=\frac{2}{5}\]. Jacob is canoeing in a river with a 2 mph current. 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? How far from home can you take a bus that travels a miles an hour, so as to return home in time if you walk back at the rate of b miles an hour? { "3.17.01:_Introducing_Rational_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.
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https://status.libretexts.org. document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); 150 Common: Difficult Idioms with Examples. Sanjay can paint a room in 5 hours. Lets look at another application of the reciprocal concept. Same time problem: Upstream-Downstream. Let x be that time. To clear fractions from this equation, multiply both sides by the common denominator 10x. In this direction, the current works WITH the boat's engine, so the rate would be y + x. For in one hour, Raymond does of the job, and Robert, . Can you determine the speed of the current and answer? Raymond can do a job in 3 hours, while it takes Robert 2 hours. However, there is variation in questions that demands more variation in formulas as well. If he puts 2/3 cups of salt and 1/2 cup of pepper in his shaker, what is the ration of salt to pepper? Thus, our two numbers are x and 2x+1. Also Read: A Guide On How to Prepare for Bank Exams. No packages or subscriptions, pay only for the time you need. The speed of the boat (in still water) is 13 miles/hour. . Jacob can paddle his kayak at a speed of 6 mph in still water. Boats and stream questions are a common topic in SSC, Bank exams, LIC, UPSC, and other competitive exams. \[\begin{aligned} 10 x^{2}-4 x-25 x+10 &=0 \\ 2 x(5 x-2)-5(5 x-2) &=0 \\(2 x-5)(5 x-2) &=0 \end{aligned}\], \[2 x-5=0 \quad \text { or } \quad 5 x-2=0\]. Let = speed of boat in still water Let = speed of current Upstream: Speed is What is the speed of the current? upstream, the current (which is C miles per hour) will be pushing against
Best Answer #1 +118288 +10 . Find the rate of the current and the rate of the boat in still water. The total time of the trip is 9 hours. Her parents names were Marie- Madel Unit 3: Instructor Graded Assignment
Solving the system of equations simultaneously, we get. However, they both lead to the same number-reciprocal pair. Therefore, the sum of their reciprocals can be represented by the rational expression 1/x + 1/(2x + 1). answered 11/14/20, Mathematics Teacher - NCLB Highly Qualified. He calculated the speed of the river that day as 1 km/hr. Answer: 1 hour 15 minutes. How long it takes the faster one. x15. {"cdnAssetsUrl":"","site_dot_caption":"Cram.com","premium_user":false,"premium_set":false,"payreferer":"clone_set","payreferer_set_title":"ASVAB Mathematics Review Part 2","payreferer_url":"\/flashcards\/copy\/asvab-mathematics-review-part-2-1574662","isGuest":true,"ga_id":"UA-272909-1","facebook":{"clientId":"363499237066029","version":"v12.0","language":"en_US"}}. A merchant borrowed $650 for one year and repaid the bank $682.50 at the end of the year. Boat ( in still water colored area cup of pepper in his shaker, what is equation! 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