Question

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

Answer 1

d = distance traveled = 1 km

w = velocity of wind

c = velocity of cyclist

when wind and cyclist move in same direction , time taken to travel distance "d" = 3 min = 3/60 h

we know that , distance/speed = time

d/(c + w) = 3/60

1/(c + w) = 3/60

c + w = 20                                                       eq-1

when wind moves opposite to cyclist  , time taken to travel distance "d" = 4 min = 4/60 h

so d/(c - w) = 4/60

1/(c - w) = 1/15

c - w = 15                                                     eq-2

adding eq-1  and eq-2

(c + w) + (c - w) = 20 + 15

2 c = 35

c = 17.5 km/h

to travel 1 km in the absence of wind , time taken is given as

t = d/c = 1/17.5 = 60/17.5 min = 3.43 min