A person travels on a cycle from home to church on a straight road with wind against him. He took 4 hours to reach there.

On the way back to the home, he took 3 hours to reach as wind was in the same direction. If there is no wind, how much time does he take to travel from home to church?

Answer

Let distance between home and church is D.

A person took 4 hours to reach church. So speed while travelling towards church is D/4.

Similarly, he took 3 hours to reach home. So speed while coming back is D/3.

There is a speed difference of 7*D/12, which is the wind helping person in 1 direction, & slowing him in the other direction. Average the 2 speeds, & you have the speed that person can travel in no wind, which is 7*D/24.

Hence, person will take D / (7*D/24) hours to travel distance D which is 24/7 hours.

Answer is 3 hours 25 minutes 42 seconds

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## 2 comments:

how is the speed difference 7*D/12 ? I did not get it..

consider the D = 48. In one direction it takes 4 hours (i.e. speed is 12 Kmph) and on return it takes 3 hours so speed is 16 kmph. The difference would be D/12, i.e. 4 kmph. May be I am missing to get the speed difference to 7*D/12..

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