REVEAL THE ANSWER
If he can cycle a mile in three minutes with the wind, he could go 1 1/3 miles in four minutes. He returns against the wind in the same four minutes, so he could go 2 1/3 miles in eight minutes, with the wind helping exactly half the time and hindering him for the other half. So, the wind can be ignored, and we conclude that on a windless day he could go 2 1/3 miles in eight minutes, or one mile in 3 and 3/7 minutes. It is incorrect to halve the total time to obtain an average speed, because one way the wind helps the cyclist for three minutes, and the other way it hinders him for four minutes. So, if you said 3 1/2 minutes, you were wrong.