Final answer:
One inlet pipe can fill the pool in 4 hours, and a drain can empty the pool in 6 hours. With the drain left open, it will take the pipe 12 hours to fill the pool.
Step-by-step explanation:
We can solve this rational equation by setting up a rate equation. Let's say the work done by the pipe in 1 hour is 1 pool (as it can fill the pool in 4 hours), and the work done by the drain in 1 hour is -1/6 (as it can empty the pool in 6 hours). Let the time taken by the pipe to fill the pool with the drain open be x.
According to the rate equation, (1/4 - 1/6) = 1/x. Solving this equation, we can find x.
By finding the least common denominator, the equation simplifies to (3/12 - 2/12) = 1/x, which is 1/12 = 1/x. Cross-multiplying, we get x = 12 hours.
Learn more about Solving rational equations