Question

It can take 12 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for 4 hours and the pipe of smaller diameter for 9 hours, only half of the pool can be filled. How long will it take for each pipe to fill the pool separately.

Answer 1

let the time taken by the first pipe be x hours and the time taken by the second pipe be y hours.

in 1 hour the first pipe can fill it = 1/x

in 1 hour the second pipe can fill it = 1/y

1/x +1/y = 1/12 --------------(1)

4/x = 9/9 =1/2---------------(2)

Consider 1/x be a and 1/y be b.

a + b = 1/12 -------------(3)

4a + 9b = 1/2 ----------------(4)

multiply 3 by equ (4) and then subtract equ(5) from equ(4).

4a + 4b =1/3 --------------(5)

we get, b = 1/30

y = 30.

sustituting the value of y in equ(3) we get

a + 1/30 = 1/12

x = 20.

Hence the first pipe would take 20hours and the second pipe woulde 30 hours