Officer Aptitude Rating (OAR) PracticeTest

If both pipes fill the pool in five hours, how long would it take the slower pipe to fill the pool alone?

1. 10 hours

2. 11.25 hours

3. 15 hours

4. 12 hours

The correct answer is: 11.25 hours

To determine how long it would take the slower pipe to fill the pool alone given that both pipes together can fill it in five hours, we first need to understand the combined work rate of both pipes. If both pipes together fill the pool in five hours, this means that their combined rate of work is 1/5 of the pool per hour. Let's denote the rate of the faster pipe as Rf and the rate of the slower pipe as Rs. The sum of their rates gives us: Rf + Rs = 1/5 Now, to find how long it would take the slower pipe to fill the pool alone, we can express Rs in terms of its filling time, which we'll denote as Ts (the time it takes for the slower pipe to fill the pool by itself). The rate of work of the slower pipe would then be: Rs = 1/Ts Replacing Rs in the combined rate equation gives: Rf + 1/Ts = 1/5 At this point, let's assume that the faster pipe fills the pool in 5 hours less time than the slower pipe. If we denote the faster pipe's filling time as Ts - 5 (assuming the faster pipe operates at a faster rate, it takes