Scenario #2: An older hose can fill a pool in 8 hours, and a newer hose can fill the same pool in 6 hours. If the pool drain was left open accidentally, but the pool still filled up in 12 hours with both hoses running, how long would it take for the drain to empty a full pool on its own?

Question

Scenario #2: An older hose can fill a pool in 8 hours, and a newer hose can fill the same pool in 6 hours. If the pool drain was left open accidentally, but the pool still filled up in 12 hours with both hoses running, how long would it take for the drain to empty a full pool on its own?

Identify common incorrect strategies used to attempt to solve this problem:

Answer 1

1. Assuming that the drainage rate of the pool is constant and subtracting the time it takes for the two hoses to fill the pool from 12 hours to determine the drainage time.

2. Not considering the fact that the hoses were running simultaneously with the drain open, affecting the overall time it took to fill the pool.
3. Using a general formula such as average rate = total work / total time to try to calculate the drainage time without taking into account the specific rates of filling and draining the pool.