If a pipe can fill a tank in 25 minutes and another pipe can empty it 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 pipe can fill a tank in 25 minutes and another pipe can empty it in 50 minutes, how long will it take to fill the tank if both pipes are opened together?
15 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 pipe can fill a tank in 25 minutes and another pipe can empty it 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: 5
Step 1: Determine the rate at which the first pipe fills the tank. 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 rate at which the second pipe empties the tank. 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. The first pipe fills at a rate of 1/25 and the second pipe empties at a rate of 1/50. So, the net rate is 1/25 - 1/50.
Step 4: Find a common denominator to subtract the rates. The common denominator for 25 and 50 is 50. Convert 1/25 to 2/50. Now, subtract: 2/50 - 1/50 = 1/50.
Step 5: 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 when both pipes are open.
