Math CentralQuandaries & Queries


Question from Hannah, a student:

The speed of a stream is 3 mph. A boat travels 10 miles upstream in the same time it takes to travel 16 miles downstream. What is the speed of the boat in still water?

Hi Hannah,

The fundamental equation is that

distance = time $\times$ rate.

Suppose that the speed of the boat in still water is $s$ mph and the time it takes to travel the 10 miles upstream is $t$ hours. Travelling upstream is travelling against the current so the going upstream the boat travels at $s - 3$ mph. Write the fundamental equation above for the trip upstream.

What is speed at which the boat travels downstream? The time downstream is the same as the stream upstream so now write the fundamental equation for the trip downstream.

Solve one of the equations for $t$ and substitute into the second equations. Solve for $s.$


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