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?
Check your solution
To solve this problem, we can first calculate the fraction of the pool that each hose can fill in one hour.
The older hose can fill 1/8 of the pool in one hour.
The newer hose can fill 1/6 of the pool in one hour.
Together, both hoses can fill 1/8 + 1/6 = 7/24 of the pool in one hour.
Since the pool fills up in 12 hours with both hoses running, this means that in one hour, the drain must be emptying 1 - 7/24 = 17/24 of the pool.
Therefore, the drain can empty the pool on its own in 24/17 hours or approximately 1.41 hours.
To check this solution, we can calculate the combined rate of filling by both hoses and draining by the pool and see if it adds up to the pool filling in 12 hours.
Older hose: 1/8 of pool in one hour
Newer hose: 1/6 of pool in one hour
Combined filling rate: 1/8 + 1/6 = 7/24 of pool in one hour
The drain is emptying 17/24 of the pool in one hour.
Together, the net rate of filling is 7/24 - 17/24 = -10/24 = -5/12 of the pool in one hour.
Since the pool is fully filled in 12 hours, the net rate of filling times 12 hours should equal 1 full pool:
(-5/12) * 12 = -5 full pool
This confirms that the pool fills up in 12 hours with both hoses running, and the drain can empty the pool on its own in approximately 1.41 hours.