Series

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?

sol>

let speed of cyclist be x kmph
let speed of wind be y kmph
then,along the wind,
speed=x+y,dist.=1 km and time=3min=1/20 hr equating,we get,x+y=20
similarly, against the wind,
speed=x-y,dist=1km and time=4min=1/15 hr, equating we get,x-y=15
using both equations we get,x=35/2
speed=35/2 kmph, dist=1km,
time=dist/speed
=1/35/2=2/35 hours=2/35*60=24/7 min





v1-v2=0.25km/mn
v1+v2=0.33km/mn
______________
2v1=0.58km/mn
v1=0.29km/mn
t=distance/velocuty
=1km/0.29km/mn
=3.44mn