Respuesta :
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 [tex]\frac{1}{t}[/tex].
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 [tex]\frac{1}{14}[/tex].
Part of pool drained by both pumps working together in one hour would be [tex]\frac{1}{6}[/tex].
Now, we will equate the sum of part of pool emptied by both pumps with [tex]\frac{1}{6}[/tex] and solve for t as:
[tex]\frac{1}{14}+\frac{1}{t}=\frac{1}{6}[/tex]
[tex]\frac{1}{14}\times 42t+\frac{1}{t}\times 42t=\frac{1}{6}\times 42t[/tex]
[tex]3t+42=7t[/tex]
[tex]7t=3t+42[/tex]
[tex]7t-3t=3t-3t+42[/tex]
[tex]4t=42[/tex]
[tex]\frac{4t}{4}=\frac{42}{4}[/tex]
[tex]t=10.5[/tex]
Therefore, it will take 10.5 hours for the newer pump to drain the pool on its own.
