: 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:
- Assuming that the drain's rate of emptying is the same as the older hose's rate of filling, and subtracting the older hose's rate from the combined rate of both hoses to calculate the drain's rate.
- Ignoring the fact that the combined rate of both hoses filling the pool is faster than the drain's rate of emptying, and trying to calculate the drain's rate in isolation.
- Incorrectly assuming that since the pool filled up in 12 hours, the drain would take 12 hours to empty the pool as well.