Math CentralQuandaries & Queries


Question from Mohanad, a student:

Howie Sorkin can travel 8 miles upstream in the same time it takes him to go 12 miles downstream. His boat goes 15 mph in still water. What is the rate of the current?


The key to this problem is that

$\mbox{ distance} = \mbox{ time} \times \mbox{ rate.}$

You have two equations, one from going upstream and the other for going downstream. The time is the same for each equation and the distances are 8 and 12 miles.

Suppose that the rate of the current is $r$ miles per hour then the boat travels downstream at $r + 15$ miles per hour. What is the speed of the boat when travelling upstream? Solve for $r.$


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