It takes 10 hours to fill a pool with water, and 20 hours to drain it. If the pool is empty and the drain is open, how long will it take to fill the pool?
To solve this problem, we need to find the rate at which the pool fills and the rate at which it drains. Once we have those rates, we can determine how long it will take to fill the pool.
Let's start with the rate at which the pool fills. We know that it takes 10 hours to fill the pool, so we can say that the filling rate is 1 pool per 10 hours, or 1/10 pool per hour.
Next, let's find the rate at which the pool drains. We're given that it takes 20 hours to drain the pool, so the draining rate is 1 pool per 20 hours, or 1/20 pool per hour.
Now, let's consider the scenario where the pool is empty and the drain is open. In this case, the pool will be filling up while also draining. To find the net rate of filling, we subtract the draining rate from the filling rate:
Filling rate - Draining rate = 1/10 - 1/20 = 1/10 - 1/20 = 2/20 - 1/20 = 1/20 pool per hour.
Since the filling rate is greater than the draining rate, the pool is filling up. Now, to determine how long it will take to fill the pool, we can use the rate:
1 pool / (1/20 pool per hour) = 20 hours.
Therefore, it will take 20 hours to fill the empty pool while the drain is open.