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?

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 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 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 xx 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.