What is the speed of the boat in still water? How many hours will it take if they work together? \[\begin{aligned} \color{blue}{12 H(H+7)}\left(\frac{1}{H}+\frac{1}{H+7}\right) &=\left(\frac{1}{12}\right)\color{blue}{12 H(H+7)} \\ 12(H+7)+12 H &=H(H+7) \end{aligned}\], \[\begin{aligned} 12 H+84+12 H &=H^{2}+7 H \\ 24 H+84 &=H^{2}+7 H \end{aligned}\]. Here are the important terms every applicant should know: Also Read: Permutation And Combination For Competitive Exams. How do we find the two equations we need? Katrina drove her car to Boston at a speed of 100 kph (kilometers per hour). Uttar Pradesh 201301, Devonshire House, 60 Goswell Road, Let's see what kinds of equations we can come up with. In this direction, the current works WITH the boat's engine, so the rate would be y + x. 1. The sum of the reciprocals of two consecutive integers is \(\frac{19}{90}\). 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. 15 / 2 = 7.5 miles . If we divide both sides of the second equation by 3,
Discarding the negative answer (speed is a positive quantity in this case), the speed of the current is 8 miles per hour. That is, Maria will complete 1/3 of a report. A boat travels at a constant speed of 3 miles per hour in still water. 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 Let x be the distance to Boston. Multiply both sides by the common denominator (32 c)(32 + c). the boat, and the boat's speed will decrease by C miles per hour. Find the number(s). The sum of the reciprocals of two consecutive even integers is \(\frac{11}{60}\). Find the rate of the current and the rate of the boat in still water. Your contact details will not be published. The speed of the current is miles per hour. \[\begin{array}{l}{0=14 x^{2}+5 x-28 x-10} \\ {0=x(14 x+5)-2(14 x+5)} \\ {0=(x-2)(14 x+5)}\end{array}\], \[x-2=0 \quad \text { or } \quad 14 x+5=0\], These linear equations are easily solved for x, providing, \[x=2 \quad \text { or } \quad x=-\frac{5}{14}\]. ---------------- Downstream DATA: What is the rate of water's current? Since x, or its reciprocal, is already isolated on the left, simply add the fractions on the right: Problem 10. The return trip 2 hours going downstream. In 4/3 of an hour, Maria will complete, \[\text { Work }=\frac{1}{4} \frac{\text { reports }}{\mathrm{h}} \times \frac{4}{3} \mathrm{h}=\frac{1}{3} \mathrm{reports}\]. 3 . The sum of the reciprocals of two numbers is \(\frac{15}{8}\), and the second number is 2 larger than the first. Example A person challenged himself to cross a small river and back. Hence, the sum of x and its reciprocal is represented by the rational expression x + 1/x. Set this equal to 7/10. That is, if x = 5/2, then its reciprocal is 2/5. Example 3. It takes Amelie 18 hours longer to complete an inventory report than it takes Jean. Find the speed of the freight train. 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. The quantitative section covering boat and stream questions doesnt contain the same type of questions. Multiply both sides of this equation by the common denominator 4t. All boat and stream questions are not the same, they can be classified into 4 types distance, average speed, speed, and time-based questions. We'll choose the easiest equation
Thus, our two numbers are x and 2x+1. Going up stream 5 miles at speed relative to shore of 8-4 = 4 mph takes 1.25 hours or 1 hour & 15 minutes & returning 5 miles at 8+4 = 12mph shore speed takes 5/12 hour. Carlos can do a certain job in three days, while it takes Alec six days. United Kingdom, EC1M 7AD, Leverage Edu More answers below Quora User Sanjay can paint a room in 5 hours. For example, in the first row, d = 60 miles and v = 3 c miles per hour. How long does it take Hank to complete the job if he works alone? Algebra questions and answers. That is, \[\text { Work }=\text { Rate } \times \text { Time. Find the two numbers. Current It takes a boat 2 hours to travel 18 miles upstream against the current. to work with: The speed of the current is 2 miles per hour. 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. \[\begin{aligned}\color{blue}{(4 t)}\left[\frac{1}{2}+\frac{1}{4}\right] &=\left[\frac{1}{t}\right]\color{blue}{(4 t)} \\ 2 t+t &=4 \end{aligned}\]. . As a result of the EUs General Data Protection Regulation (GDPR). How long will it take them to finish the report if they work together? Let x =
No packages or subscriptions, pay only for the time you need. The relation t = d/v can be used to compute the time entry in each row of Table \(\PageIndex{1}\). It takes Ricardo 8 hours longer to complete an inventory report than it takes Amelie. Uttar Pradesh 201301, Devonshire House, 60 Goswell Road, 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. So now we have a second equation: 2(y+x) = 100. 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. The sum of the reciprocals of the two numbers is 7/10. Rate problems are based on the relationship Distance
where d represents the distance traveled, v represents the speed, and t represents the time of travel. If they work together, how long will it take them? However, as we saw above, the rates at which they are working will add. Solution : Speed of the boat in still water = 30 km/hr. Unit 3 focuses on interest and loan concepts covered in your reading of Chapter 11: Si Fractions We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. However, the last row of Table \(\PageIndex{6}\) indicates that the combined rate is also 1/t reports per hour. Copyright 2021, Leverage Edu. What is the speed of the current in miles per hour. The speed of the boat (b) in still water is 10 miles/hour and the rate of the current (c) is 8 miles/hour. The same boat can travel 36 miles downstream in 3 hours. The sum of the reciprocals of two consecutive odd integers is \(\frac{16}{63}\). A club has 4 Blue kites, 3 Green kites, and 3 Yellow kites. Then. document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); 150 Common: Difficult Idioms with Examples. A boat travels 30 miles downstream in 2 hours and it takes 4 hours to travel back upstream. Using the relation , distance = speed x time, we get. Thus, the equation we seek lies in the Rate column of Table \(\PageIndex{6}\). the chart for the time upstream. Find the number(s). We can make the numbers a bit smaller by noting that both sides of the last equation are divisible by 10. __________________ 3. How many hours would it take Sanjay if he worked alone? Therefore, The rate of current is, Hence, The required rate of current is 1.6. Find the speed of the current and the speed of the boat 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 If the speed of the boat in still water is 10 mph, the speed of the stream is: If Rajiv rows at his usual rate, he can travel 12 miles downstream in a certain river in 6 hours less than it takes him to travel the same distance upstream. This last equation is nonlinear, so make one side zero by subtracting 24H and 84 from both sides of the equation. Jacob is canoeing in a river with a 5 mph current. It takes Sanjay 9 hours to paint the same room. . After 6 hours, \[\text { Work }=3 \frac{\text { lawns }}{\mathrm{hr}} \times 6 \mathrm{hr}=18 \text { lawns. The total time of the trip is 9 hours. it's moving upstream and downstream on a river. For Free. This was all about the Boats and streams formula. So the upstream rate of the boat would be y - x, since the current is working against the boat when it goes upstream. \[\begin{aligned} 180 c &=180 \\ c &=1 \end{aligned}\]. upstream, the current (which is C miles per hour) will be pushing against
How tall is the tower? the speed of the boat in still water? distance = rate * time UPSTREAM 9 r-3 DOWNSTREAM 11 r+3 Time= distance/rate EQUATION: Time up = Time down or 1/12 of a kitchen per hour. A train travels 30 mi/hr faster than a car. If they work together, it takes them 10 hours. 2(b + c) = 128. b - c = 32. b . | CE Board Problem in Mathematics, Surveying and Transportation Engineering Home Date of Exam: November 2018 Subject: Moira can paddle her kayak at a speed of 2 mph in still water. To set up an equation, we need to use the fact that the time to travel upstream is twice the time to travel downstream. \[\begin{array}{l}{0=H^{2}+7 H-24 H-84} \\ {0=H^{2}-17 H-84}\end{array}\]. Find the speed of the freight train. a. Delhi 110024, A-68, Sector 64, Noida, Boris is kayaking in a river with a 6 mph current. A boat takes 2 hours to travel 15 miles upriver against the current. We are not permitting internet traffic to Byjus website from countries within European Union at this time. Round your answer to the nearest hundredth. Clearly, working together, Bill and Maria will complete 2/3 + 1/3 reports, that is, one full report. answered 02/17/15. Round your answer to the nearest hundredth. A man has painted 1/5 of a tower. A link to the app was sent to your phone. Solution. To organize our work, we'll make a chart of the distance,
Block A, Defence Colony, New Delhi, A boat travels a distance of 80 km in 4 hours upstream and same distance down stream in 2 hours in a river. Expand, simplify, make one side zero, then factor. We know that if the boat were on a still lake, its motor would propel it
Step-by-step solution Chapter 2.2, Problem 85P is solved. The integer pair {4, 21} has product 84 and sums to 17. {\(\frac{2}{3}\), \(\frac{8}{3}\)} and {\(\frac{8}{5}\), \(\frac{2}{5}\)}. Answer: 1 hour 15 minutes. An OTP has been sent to your registered mobile no. You have created 2 folders. That is, together they work at a rate of 1/t reports per hour. The same boat can travel 36 miles downstream in 3 hours. Suppose that he can ca- noe 2 miles upstream in the same amount of time as it takes him to canoe 5 miles downstream. Let x be the speed of the train. This is reflected in the entries in the first row of Table \(\PageIndex{5}\). 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. Lets look at some applications that involve the reciprocals of numbers. Best Answer #1 +118288 +10 . If they work together, it takes them 3 hours. Jacob is canoeing in a river with a 2 mph current. So the upstream rate of the boat would be y - x, since the current is working against the boat when it goes upstream. Jean can paint a room in 4 hours. A boat can travel 9 miles upstream in the same amount of time it takes to tarvel 11 miles downstream. .85 x 60 (minuntes in 1 hour) = 50 minutes. It travels 150 miles upstream against the current then returns to the starting location. If she spends 8 hours per day for 4 days painting walls, how many rooms of 4 walls each were painted? 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 You have exactly h hours at your disposal. When traveling downstream speed = boat + current = 20miles in 2 hours = 10miles/hour. Let t represent the time it takes them to complete 1 report if they work together. Mr. Larlham }\], A second important concept is the fact that rates add. 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a boat takes 2 hours to travel 15 miles upstream against the current