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?

Solution:

3 hours 25 minutes 42 seconds

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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.

## 7 comments:

Answer is 3 hours 25 minutes 42 seconds .

Answer is 3 hours 25 min 42 sec

d= distance;

x=cyclist speed;

y=wind speed;

d/4 = x-y;

d/3 = x+y;

x-y)+(x+y) =(d/4)+(d/3);

2x = 7d/12;

x = 7d/24;

time to travel d distance without wind t = d/(7d/24) hours

t = 24/7 hours

t = 3 + 3/7 hours

t = 3 hours 25 min 42 sec.

here goes the answer..

3.42hr..i.e 3hr 25min 42 sec..

(x-y)4=(x+y)3

hence x=7y..(1)

xt=distance travelled(D)...(2)

keep it in the equation (x-y)4=D and substitute x by 7y..

we will get t=24/7..

let his speed be 's' and wind's speed b 'w'...

(w+s)/(w-s)=4:3

s=7w

dist=4hrs*(7w-w)

=24w

time taken when no wind= 24w/7w

=24/7 hrs

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