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?

For Solution SCROLL DOWN...


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.


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.


here goes the answer..
3.42hr..i.e 3hr 25min 42 sec..
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'...

time taken when no wind= 24w/7w
=24/7 hrs

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