[12.6 min] Jack and Jill went up and down a hill. They started from the bottom and Jack met Jill again 20 miles

Jack and Jill went up and down a hill. They started from the bottom and Jack met Jill again 20 miles from the top while returning. Jack completed the race 1 min a head of Jill. If the hill is 440 miles high and their speed while down journey is 1.5 times the up journey. How long it took for the Jack to complete the race ?

12.6 min

14.6 min

18.2 min

12.4 min

Explanation:

Assume that height of the hill is 440 miles.

Let speed of Jack when going up = x miles/minute

and speed of Jill when going up = y miles/minute

Then speed of Jack when going down = 1.5x miles/minute

and speed of Jill wen going up = 1.5y miles/minute

Case 1 :

Jack met jill 20 miles from the top. So Jill travelled 440 - 20 = 420 miles.

Time taken for Jack to travel 440 miles up and 20 miles down = Time taken for Jill to travel 420 miles up

440x+201.5x=420y440x+201.5x=420y

681.5x=420y681.5x=420y

68y = 63x

y = 63x6863x68 ---(1)

Case 2 :

Time taken for Jack to travel 440 miles up and 440 miles down = Time taken for Jill to travel 440 miles up and 440 miles down - 1

440x+4401.5x=440y+4401.5y440x+4401.5x=440y+4401.5y - 1

440×53(1y−1x)=1440×53(1y−1x)=1-----(2)

Substitute (2) in (1) we get

x = 440×5×53×6340×5×53×63

t = 440×53(1x)440×53(1x)

t = 12.6min.

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