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 lon 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 lon 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. Some may incorrectly add the rates at which the two hoses fill the pool (1/8 + 1/6) and then try to calculate the time it would take for both hoses and the drain to fill the pool together rather than emptying it.

2. Some may calculate the time it would take for the drain to empty the pool based on the combined rate at which the hoses fill the pool and the drain empties it without considering the individual rates of filling and emptying.
3. Some may mistakenly calculate the time it would take for the pool to fill with both hoses running at the same time and then try to subtract that time from 12 hours to find the time it would take for the drain to empty the pool.