A cyclist drove one kilometre, with the wind in his back, in three minutes and…
2023
A cyclist drove one kilometre, 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 kilometre without wind?
- A.
34/7 min
- B.
54/7 min
- C.
14/7 min
- D.
24/7 min
Attempted by 9 students.
Show answer & explanation
Correct answer: D
Let v be the cyclist's speed in still air (km/min) and w be the wind's effect (km/min).
With the wind: v + w = 1/3 (km per minute).
Against the wind: v - w = 1/4 (km per minute).
Add the two equations to eliminate w:
2v = 1/3 + 1/4 = 7/12, so v = 7/24 km/min.
Time for 1 km without wind: time = 1 / v = 1 / (7/24) = 24/7 minutes.
Answer: 24/7 minutes.