Bunuel
A boatman rows to a place 48 km distant and back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. Find the rate of the stream.
A. 1 km/h
B. 2 km/h
C. 3 km/h
D. 4 km/h
E. 5 km/h
You could go through the trouble of setting up equations and solving them. But if you think about it, you can use the fact that the distances with and against the stream are the same to make the problem much easier.
Since the distances are the same, the rates will be inversely proportional to the times. (Note: this wouldn't work if the distances were different each way.) Since the ratio for rates is 4:3, the times will be 3:4. Therefore, the time will be:
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Time, with stream: \(\frac{3}{7} × 14 = 6\) hours
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Time, against stream: \(\frac{4}{7} × 14 = 8\) hours
By the formula \(Rate = \frac{Distance}{Time}\), you get
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Rate, with stream: \(\frac{48}{6} = 8\) km/h
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Rate, against stream: \(\frac{48}{8} = 6\) km/h
Don't be fooled into thinking the answer is 2. The stream adds for the with-stream rate and subtracts for the against-stream rate. So, the no-stream rate must be 7 km/h and the speed of the stream must be
(A) 1 km/h.