Final answer:
The total time to fill the swimming pool with both pipes, accounting for the hot water pipe turned on 3 hours later is 3 hours and 36 minutes.
Step-by-step explanation:
To solve this problem, we need to determine the rate at which each water pipe fills the swimming pool when both are working together. First, we calculate the rate at which the cold water pipe fills the pool: since it can fill the pool in 4 hours, its rate is 1/4 pool per hour. Similarly, the hot water pipe fills the pool at a rate of 1/6 pool per hour.
Since the hot water pipe is turned on 3 hours after the cold water pipe, the cold water pipe alone would have filled 3/4 of the swimming pool in that time (3 hours × 1/4 pool/hour).
This leaves 1/4 of the swimming pool to be filled.
When both pipes work together, they fill the pool at a combined rate of 1/4 + 1/6 = 5/12 pools per hour.
To fill the remaining 1/4 of the pool, we divide the remaining volume by the combined rate: 1/4 pool / 5/12 pools per hour = 3/5 hours, which is 36 minutes.
Adding the initial 3 hours during which the cold water pipe was running alone to the 36 minutes they both ran together gives us a total time of 3 hours and 36 minutes to fill the pool completely.
Hence, the total time to fill the swimming pool with both pipes, accounting for the hot water pipe turned on 3 hours later is 3 hours and 36 minutes.