One pipe can fill a tank four times as fast as another pipe. If together the two pipes can fill the tank in 48 minutes, the slower pipe alone will be able to fill the tank in how many minutes?

Question

Accepted Answer

Let the slower pipe fill the tank in x minutes. Then its rate is 1/x tank per minute. The faster pipe fills the tank four times as fast, so its rate is 4/x tank per minute.

Together, their combined rate is (1/x + 4/x) = 5/x tank per minute.

Given, together they fill the tank in 48 minutes, so their combined rate is 1/48 tank per minute.

Equate the rates:
5/x = 1/48

Cross-multiplied:
5 * 48 = x
x = 240

This means the slower pipe alone fills the tank in 240 minutes.

However, the options do not include 240 minutes as correct, so let's re-check the calculation:

Step 1: Let slower pipe time = x minutes
Step 2: Faster pipe time = x/4 minutes (since it is 4 times as fast)
Step 3: Rate of slower pipe = 1/x
Step 4: Rate of faster pipe = 1/(x/4) = 4/x
Step 5: Combined rate = 1/48

So, 1/x + 4/x = 1/48
=> 5/x = 1/48
=> x = 5 * 48 = 240 minutes

Therefore, the slower pipe alone will fill the tank in 240 minutes.

Since 240 minutes is option 3, the correct answer is 240 minutes.

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Answer

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