A motorboat moves 16 miles per hour in still water. It travels 15 miles upstream and 15 miles downstream in a total time of 2 hours. What is the speed of the current?

Let c=speed of current, so the effective upstream speed against the current is 16-v and with the current downstream is 16+c. The distances travelled are 15 miles in each case.

Distance=speed times time, so time=distance/speed and the combined times for upstream and downstream:

15/(16-c)+15/(16+c)=2, so 15(16+c)+15(16-c)=2(16²-c²), 480=512-2c², c²=(512-480)/2=32/2=16 so c=4mph.

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