Question

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

Answer 1

Let time taken to fill the pool by the larger diameter pipe = x hr and time taken to fill the pool by the smaller diameter pipe = y hr.

According to the question,

`1/x + 1/y = 1/12`   ...(i)

And `4/x + 9/y = 1/2`   ...(ii)

Multiplying by 9 in equation (i) and subtracting from equation (ii), we get

`4/x + 9/y = 1/2`

`4/x + 9/y = 9/12`

   (–)    (–)     (–)

`(-5)/x = 1/2 - 9/12 = (-3)/12`

⇒ 3x = 12 × 5

⇒ x = 20

Putting the value of x in equation (i), we get

`1/20 + 1/y = 1/12`

⇒ `1/y = 1/12 - 1/20`

⇒ `1/y = (5 - 3)/60`

⇒ `1/y = 2/60`

⇒ `1/y = 1/30`

⇒ y = 30

Hence, time taken to fill the fool by the larger and smaller diameter pipe respectively 20 hrs and 30 hrs.