A motorboat can maintain a constant speed of 13 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 63 minutes; the return trip takes 15 minutes. What is the speed of the current?

The speed in each direction is the speed of the boat with the speed of the current appropriately added. If x is the speed of the current, the upstream speed is 13-x; the downstream speed is 13+x.

The ratio of times is inversely proportional to the ratio of speeds, so we ahve ...

15/63 = 5/21 = (13-x)/(13+x)

5(13 +x) = 21(13 -x) . . . . . . . cross multiply

26x = 13(21 -5) = 13·16

x = 13·16/26 = 16/2 = 8

The speed of the current is 8 miles per hour.

A motorboat can maintain a constant speed of 13 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 63 ​minutes; the return trip takes 15 minutes. What is the speed of the​ current?

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A motorboat can maintain a constant speed of 13 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 63 minutes; the return trip takes 15 minutes. What is the speed of the current?