Question

One pipe can fill a tank three times as fast as another pipe. If the two pipes together can fill the tank in 36 minutes,then the slower pipe will take how much time to fill the tank alone?

• A. 81 minutes
• B. 108 minutes
• C. 192 minutes
• D. 144 minutes

Answer 1

The Correct Option is D

To solve this problem, we need to determine the time taken by the slower pipe to fill the tank alone. Let's break this down step-by-step:

1. Let's denote the time taken by the slower pipe to fill the tank alone as \(x\) minutes.
2. Since one pipe can fill the tank three times as fast as the slower pipe, the faster pipe’s time to fill the tank alone will be \(\frac{x}{3}\).
3. According to the problem, both pipes together fill the tank in 36 minutes. Therefore, their combined rate of working is filling 1 tank/36 minutes.
4. The combined rate of filling the tank can also be expressed in terms of their individual rates. The rate of filling by the slower pipe is \(\frac{1}{x}\) (as it fills the tank in \(x\) minutes), and the rate of the faster pipe is \(\frac{3}{x}\) (as it fills the tank in \(\frac{x}{3}\) minutes).
5. Therefore, the combined rate is:
6. Since we know that together they fill the tank in 36 minutes, we equate the combined rate:
7. To find \(x\), solve the equation:
8. Thus, the slower pipe will take 144 minutes to fill the tank alone.

This confirms that the correct answer is indeed 144 minutes.