Respuesta :
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 [tex]\frac{1}{t}[/tex].
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 [tex]2t[/tex].
Part of waste released by plant 2 in one hour would be [tex]\frac{1}{2t}[/tex].
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 [tex]\frac{1}{4}[/tex].
[tex]\frac{1}{t}+\frac{1}{2t}=\frac{1}{4}[/tex]
[tex]\frac{1}{t}\cdot 4t+\frac{1}{2t}\cdot 4t=\frac{1}{4}\cdot 4t[/tex]
[tex]4+2=t[/tex]
[tex]t=6[/tex]
Therefore, it will take 6 hours for the faster plant to fill the tank working alone.
