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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.

7 comments:

Scrutabilis said...

Answer is 3 hours 25 minutes 42 seconds .

pg... said...

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.

BANKE BIHARI said...

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..

Viral said...

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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