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?
Practice Questions
1 question
Q1
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
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: 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?
Solution: The net rate is 1/25 - 1/50 = 1/50. Therefore, it will take 50 minutes to fill the tank.
Steps: 6
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.
