A cyclist drove one kilometer, with the wind in his back, in three minutes and drove the same way back, against the wind in four minutes. If we assume that the cyclist always puts constant force on the pedals, how much time would it take him to drive one kilometer without wind?

Assuming the cyclist speed without the wind = a  and the wind speed = b

Then $$\ \frac{\ 1km}{a+b}$$ = 3   => a+b = $$\ \frac{\ 1}{3}$$

$$\ \frac{\ 1km}{a-b}$$ = 4  => a-b = $$\ \frac{\ 1}{4}$$

Adding both the equations, we get 2a = $$\ \frac{\ 1}{3}$$ + $$\ \frac{\ 1}{4}$$

=> a = $$\ \frac{\ 7}{24}$$  

Time taken to cover 1 km = $$\ \frac{\ 1\ km}{a}$$ = $$\ \dfrac{\ 1\ km}{\ \frac{\ 7}{24}}$$ = $$\ \frac{\ 24}{\ \ 7}$$ = $$3\frac{3}{7}$$