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?
First, we need to determine the combined rate at which both hoses can fill the pool.
Rate of older hose = 1 pool / 8 hours = 1/8
Rate of newer hose = 1 pool / 6 hours = 1/6
Combined rate of both hoses = 1/8 + 1/6 = 3/24 + 4/24 = 7/24 pools per hour
Since the pool filled up in 12 hours with both hoses running, the total amount of pool filled in 12 hours = 12 * (7/24) = 3.5 pools
Therefore, the amount drained by the pool drain in these 12 hours = 3.5 pools
So, the rate at which the pool was drained by the drain = 3.5 pools / 12 hours = 7/24 pools per hour
Now, since the drain was draining the pool to make it fill up in 12 hours instead of the usual 6 or 8 hours, we can assume that the drain was draining at the same rate as its filling rate.
Thus, the drain can empty a full pool on its own in 24/7 hours = 3.43 hours
Therefore, it would take the drain approximately 3.43 hours to empty a full pool on its own.