Working together, two pumps can drain a certain pool in 3 hours. If it takes the older pump 9 hours to drain the pool by itself, how long will it take the newer pump to drain the pool on its own?
Do not do any rounding.
Let the time it takes for the newer pump to drain the pool by itself be x hours.
The rate at which the older pump can drain the pool by itself is 1/9 pool per hour.
The rate at which the two pumps together can drain the pool is 1/3 pool per hour.
So, the rate at which the newer pump can drain the pool by itself is 1/x pool per hour.
Since the two pumps together can drain the pool in 3 hours, we have the equation:
1/9 + 1/x = 1/3
Multiplying through by 9x, we get:
x + 9 = 3x
2x = 9
x = 4.5
Therefore, it will take the newer pump 4.5 hours to drain the pool by itself.