The water from one outlet, flowing at a constant rate…
This problem is called a combined work problem. In these problems we use the formula:
Work (of machine 1) + Work (of machine 2) = Total Work Done
In this particular problem we can define “machine” as “outlet”. We are given that the water from one outlet, flowing at a constant rate, can fill a swimming pool in 9 hours and that the water from a second outlet, flowing at a constant rate, can fill the same pool in 5 hours. This means the hourly rate for one outlet is 1/9 pool per hour and the rate of the other outlet is 1/5 pool per hour. We also are told that the two outlets work together to fill the pool. Thus they both work together for “T” hours. We can fill these values into a simple table.
We can plug in the two work values for outlet one and outlet two into the combined worker formula.
Work (of outlet 1) + Work (of outlet 2) = Total Work Done
T/9 + T/5 = 1
To eliminate the need for working with fractions, let’s multiply the entire equation by 45.
45(T/9 + T/5 = 1)
5T + 9T = 45
14T = 45
T = 45/14 = 3 3/14 ≈ 3.21 hours