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

Answer:

6 hours.

Step-by-step 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 $\frac{1}{t}$.  

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 $\frac{1}{2t}$.  

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 $\frac{1}{4}$.

$\frac{1}{t}+\frac{1}{2t}=\frac{1}{4}$

$\frac{1}{t}\cdot 4t+\frac{1}{2t}\cdot 4t=\frac{1}{4}\cdot 4t$

$4+2=t$

$t=6$

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