A cyclist drove one kilometre, with the wind in his back, in 3 minutes and drove the same way back, against the wind, in 4 minutes. If we assume that the cyclist always puts constant force on the pedals, how much time would it take him to drive 1 km without wind ?

Solution (By Examveda Team)

Let the cyclist's speed without wind be x km/hr
And the speed of the wind be y km/hr
Then,
$$\eqalign{ & \Rightarrow \frac{1}{{x + y}} = \frac{3}{{60}} \cr & \Rightarrow x + y = 20.....(i) \cr} $$
And
$$\eqalign{ & \Rightarrow \frac{1}{{x - y}} = \frac{4}{{60}} \cr & \Rightarrow x - y = 15.....(ii) \cr} $$
Adding (i) and (ii), we get:
2x = 35 or x = 17.5
Putting x = 17.5 in (i), we get : y = 2.5
Time taken to drive 17.5 km without wind = 1 hr
Time taken to drive 1 km without wind
$$\eqalign{ & = \left( {\frac{1}{{17.5}}} \right){\text{ hr}} \cr & {\text{ = }}\left( {\frac{1}{{17.5}} \times 60} \right){\text{ min}} \cr & {\text{ = 3}}\frac{3}{7}{\text{ min}} \cr} $$