Question

It takes 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 is used for 9 hours, only half of the pool is filled. How long would each pipe take to fill the swimming pool ?

Answer 1

Let the pipe with larger diameter and smaller diameter be pipes A and B respectively.
Also, let pipe A work at a rate of x hours/ unit and pipe B work at a rate of Y hours / unit.
According to the question,
x + y = `1/12` 
⇒ 12x + 12y = 1                    ....(1)
and
4x + 9y = `1/2`
⇒ 8x + 18y = 1                     ...(2)

Multiply (1) by 2 and (2) by 3, We get
24x + 24y = 2                       ...(3)
24x + 54y = 3                       ....(4)

Subtracting equation (4) from (3),
        24x + 24y = 2
-       24x + 54y = 3    
       -       -          -      
                - 30y = - 1
                      y = `1/30`
Putting y = `1/30` in equation (1)
12x + 12y = 1
∴ 12x + 12 x `1/30` = 1
∴  12x + `2/5` = 1
∴  12x = 1 - `2/5`
∴  x = `3/5 xx 1/12`
∴  x = `1/20`

Hence, the pipe with larger diameter will take 20 hours to fill the swimming pool and the pipe with smaller diameter will take 30 hours to fill the swimming pool.