Pipe A can fill a tank in 20 minutes and Pipe B can empty the same tank in 30 minutes. Find the time taken to fill the empty tank if both pipes are opened together.
Pipe A can fill a tank in 20 minutes and Pipe B can empty the same tank in 30 minutes. Find the time taken to fill the empty tank if both pipes are opened together.
A40 mins
B50 mins
C70 mins
D60 mins
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Correct Answer: 60 mins
Explanation:
Pipe A can fill a tank in 20 minutes, so its rate is \( \frac{1}{20} \) tanks per minute. Pipe B can empty the tank in 30 minutes, so its rate is \( -\frac{1}{30} \) tanks per minute (negative because it's emptying). When both pipes are opened together, their rates add up:
\(\frac{1}{20} - \frac{1}{30} = \frac{3}{60} - \frac{2}{60} = \frac{1}{60}\) tanks per minute
The combined rate is \( \frac{1}{60} \) tanks per minute. To fill one tank, the time required is the reciprocal of the rate:
\( \text{Time} = \frac{1}{\frac{1}{60}} = 60 \) minutes
Therefore, the time taken to fill the empty tank when both pipes are opened together is 60 minutes.
Final Answer: \(\boxed{60}\text{ minutes}\)
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