A tank can be filled by a pipe in 25 minutes and emptied by another pipe in 50 minutes. If both pipes are opened together, how long will it take to fill the tank?
Practice Questions
1 question
Q1
A tank can be filled by a pipe in 25 minutes and emptied by another pipe in 50 minutes. If both pipes are opened together, how long will it take to fill the tank?
16.67 minutes
20 minutes
25 minutes
30 minutes
The net rate is 1/25 - 1/50 = 1/50. Therefore, it will take 50 minutes to fill the tank.
Questions & Step-by-step Solutions
1 item
Q
Q: A tank can be filled by a pipe in 25 minutes and emptied by another pipe in 50 minutes. If both pipes are opened together, how long will it take to fill the tank?
Solution: The net rate is 1/25 - 1/50 = 1/50. Therefore, it will take 50 minutes to fill the tank.
Steps: 8
Step 1: Understand that one pipe fills the tank in 25 minutes. This means it fills 1/25 of the tank in one minute.
Step 2: Understand that the other pipe empties the tank in 50 minutes. This means it empties 1/50 of the tank in one minute.
Step 3: Calculate the net effect when both pipes are open. The filling pipe adds 1/25 of the tank per minute, and the emptying pipe removes 1/50 of the tank per minute.
Step 4: Find a common denominator to combine the two rates. The common denominator for 25 and 50 is 50.
Step 5: Convert the filling rate: 1/25 = 2/50. So, the filling pipe adds 2/50 of the tank per minute.
Step 6: Now, subtract the emptying rate from the filling rate: 2/50 - 1/50 = 1/50.
Step 7: The net rate of filling the tank is 1/50 of the tank per minute.
Step 8: To find out how long it takes to fill the entire tank, take the reciprocal of the net rate: 1 divided by (1/50) equals 50 minutes.
