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# Travel

Puzzle:

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?

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Solution:

3 hours 25 minutes 42 seconds

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.