If a tank can be filled by a pipe in 25 minutes and emptied by another pipe in 5

Practice Questions

If a tank can be filled by a pipe in 25 minutes and emptied by another pipe in 50 minutes, how long will it take to fill the tank if both pipes are opened together?

16.67 minutes
20 minutes
25 minutes
30 minutes

Questions & Step-by-Step Solutions

If a tank can be filled by a pipe in 25 minutes and emptied by another pipe in 50 minutes, how long will it take to fill the tank if both pipes are opened together?

Correct Answer: 50 minutes

Step 1: Determine the filling rate of the first pipe. It fills the tank in 25 minutes, so its rate is 1 tank per 25 minutes, or 1/25 of the tank per minute.
Step 2: Determine the emptying rate of the second pipe. It empties the tank in 50 minutes, so its rate is 1 tank per 50 minutes, or 1/50 of the tank per minute.
Step 3: Calculate the net rate when both pipes are opened together. This is done by subtracting the emptying rate from the filling rate: (1/25) - (1/50).
Step 4: To subtract these fractions, find a common denominator. The common denominator for 25 and 50 is 50. Convert 1/25 to 2/50.
Step 5: Now subtract: (2/50) - (1/50) = (2 - 1)/50 = 1/50.
Step 6: The net rate of filling the tank is 1/50 of the tank per minute. This means it takes 50 minutes to fill the entire tank.

Rate of Work – Understanding how to calculate the rate at which a tank can be filled or emptied by different pipes.
Combined Rates – Calculating the net effect of multiple rates working together, including both filling and emptying.

If a tank can be filled by a pipe in 25 minutes and emptied by another pipe in 5

Practice Questions

Questions & Step-by-Step Solutions

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