Answer:
10.5 hours.
Step-by-step explanation:
Please consider the complete question.
Working together, two pumps can drain a certain pool in 6 hours. If it takes the older pump 14 hours to drain the pool by itself, how long will it take the newer pump to drain the pool on its own?
Let t represent time taken by newer pump in hours to drain the pool on its own.
So part of pool drained by newer pump in one hour would be
.
We have been given that it takes the older pump 14 hours to drain the pool by itself, so part of pool drained by older pump in one hour would be
.
Part of pool drained by both pumps working together in one hour would be
.
Now, we will equate the sum of part of pool emptied by both pumps with
and solve for t as:
![\frac{1}{14}+\frac{1}{t}=\frac{1}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B14%7D%2B%5Cfrac%7B1%7D%7Bt%7D%3D%5Cfrac%7B1%7D%7B6%7D)
![\frac{1}{14}\times 42t+\frac{1}{t}\times 42t=\frac{1}{6}\times 42t](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B14%7D%5Ctimes%2042t%2B%5Cfrac%7B1%7D%7Bt%7D%5Ctimes%2042t%3D%5Cfrac%7B1%7D%7B6%7D%5Ctimes%2042t)
![3t+42=7t](https://tex.z-dn.net/?f=3t%2B42%3D7t)
![7t=3t+42](https://tex.z-dn.net/?f=7t%3D3t%2B42)
![7t-3t=3t-3t+42](https://tex.z-dn.net/?f=7t-3t%3D3t-3t%2B42)
![4t=42](https://tex.z-dn.net/?f=4t%3D42)
![\frac{4t}{4}=\frac{42}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B4t%7D%7B4%7D%3D%5Cfrac%7B42%7D%7B4%7D)
![t=10.5](https://tex.z-dn.net/?f=t%3D10.5)
Therefore, it will take 10.5 hours for the newer pump to drain the pool on its own.