Acyclist pedaling at a steady rate travels 30 miles with the wind. he can travel only 18 miles against the wind in the same amount of time. if the rate of the wind is 3 mph, what is the cyclist's rate without the wind?

So.. traveling without the wind, let's say the pedalist has a speed of "r"

with the wind, the wind's rate is added to it, so, he's not going "r" fast, he's really going r+3 fast

against the wind, he's going r - 3 fast

notice, he covers 30 miles with it, and 18 miles against BUT the time for both ways is the same, say time "t"

now, recall your d = rt, distance = rate * time

thus 

solve for "r"