Question

Two chemical plants are releasing waste into a holding tank. Plant 1 releases waste twice as fast as plant 2. Together they fill the tank in 4 hours. How long would it take the faster plant to fill the tank working alone?

Answer 1

6 hours.

Explanation:

Let t represent time taken by plant 1 in hours to release the waste.

Part of waste released by plant 1 in one hour would be
`(1)/(t)`.

We have been given that two chemical plant 1 releases waste twice as fast as plant 2, so time taken by plant 2 to release the waste would be
`2t`.

Part of waste released by plant 2 in one hour would be
`(1)/(2t)`.

We are also told that together they fill the tank in 4 hours. So part of tank filled by both plants working together in one hour would be
`(1)/(4)`.

`(1)/(t)+(1)/(2t)=(1)/(4)`

`(1)/(t)\cdot 4t+(1)/(2t)\cdot 4t=(1)/(4)\cdot 4t`

`4+2=t`

`t=6`

Therefore, it will take 6 hours for the faster plant to fill the tank working alone.