Let

v = the speed of the boat in still water, v>0

c = 5 mph speed of a stream

d1 = 3 miles the distance he travels upstream

d2 = 13 miles the distance he travels downstream

Downstream speed: v + c = v + 5

Upstream speed: v - c = v - 5

The time of the travel upstream = The time of the travel downstream

Since speed = distance/time we have time = distance/speed thus we have:

d1/(v - c) = d2/(v + c)

3/(v - 5) = 13/(v + 5)

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click here to see the equation solved for v

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v = 8 mph

The speed of the boat in still water is 8 mph.