Question

A cold water pipe can fill a swimming pool in 4 hrs, and a hot water pipe can fill it in 6 hrs. If cold water pipe is turned on and hot water pipe is turned on 3 hrs later, how long will it take for the pool to be filled?

Answer 1

To determine the time it will take for the pool to be filled when both a cold water pipe and a hot water pipe are used, we set up an equation based on their respective filling rates. Solving the equation reveals that the swimming pool will be filled in 3.6 hours with both pipes turned on.

Step-by-step explanation:

To solve this problem, we can use the concept of rates at which the pipes fill the pool. The cold water pipe fills the pool in 4 hours, which means it fills 1/4 of the pool in one hour. Let's assume the total time taken to fill the pool with both pipes open is t hours. In those t hours, the cold water pipe has been running the entire time, contributing 1/4 of the pool per hour. The hot water pipe, however, starts 3 hours later, so it only runs for t - 3 hours. We can represent this with the equation:

1/4 * t + 1/6 * (t - 3) = 1

Solving for t:

1. Multiply both sides by 12 (the least common multiple of 4 and 6) to get rid of the fractions:
2. 3t + 2(t - 3) = 12
3. 3t + 2t - 6 = 12
4. 5t - 6 = 12
5. Add 6 to both sides: 5t = 18
6. Divide by 5: t = 18/5 or 3.6 hours

The pool will be filled in 3.6 hours with both pipes turned on.

Answer 2

Answer: 3 hours 36 minutes

Step-by-step explanation:

You can find out that the cold pipe fills up the pool by 1/4 every hour from the question. if you turn on the cold pipe for 3 hours, the pool would be filled 3/4 before you turn on the hot water. you also can find out that the hot pipe fills up the pool 1/6 every hour. so the next hour will continue to fill up the pool 5/12 until you turn off the water. you only need to fill up the pool 1/4 more so it will take a total of 3 hours and 36 minutes to fill up.