Working together, two pumps can drain a certain pool in 5 hours. if it takes the older pump 15 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. hours

There is a formula:
(Pump1 Time * Pump2 Time) / (Pump1 Time + Pump2 Time) = Total Time
Let's say Pump 1 is the old pump
(15 * Pump2 Time) / (15 + Pump2 Time) = 5 Hours
Solving for Pump 2 time
Pump 2 time = (Pump 1 time * Total Time) / (Pump 1 time - Total Time)
Pump 2 time = (15 * 5) / (15 - 5)
Pump2 time = 75 / 10
Pump2 time = 7.5 Hours
and Happy New Year

Double Check
(15 * 7.5) / (15 + 7.5) = Total Time
112.5 / 22.5 = 5 Hours Total

The vertex of the quadratic function is (1.5, -.75)