Let

v = the speed of the boat in still water, v>0
c = 3 mph speed of the stream
d1 = 240 miles the distance he travels upstream
d2 = 300 miles the distance he travels downstream

Time of the travel upstream = Time of the travel downstream

Downstream speed: v + c
Upstream speed: v - c

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

For the upstream travel the time is:

t = d1/(v - c)

t = 240/(v - 3)

For the downstream travel the time is:

t = d2/(v + c)

t = 300/(v + 3)

Time of the travel upstream = Time of the travel downstream

240/(v - 3) = 300/(v + 3)

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click here to see the equation solved for v

........

v = 27 mph

The speed of the boat in still water is 27 miles per hour.