If a pipe can fill a tank in 20 minutes and another pipe can empty it in 30 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 20 minutes and another pipe can empty it in 30 minutes, how long will it take to fill the tank if both pipes are opened together?
10 minutes
15 minutes
20 minutes
25 minutes
The net rate is 1/20 - 1/30 = 1/60. Therefore, it will take 60 minutes to fill the tank.
Questions & Step-by-step Solutions
1 item
Q
Q: If a pipe can fill a tank in 20 minutes and another pipe can empty it in 30 minutes, how long will it take to fill the tank if both pipes are opened together?
Solution: The net rate is 1/20 - 1/30 = 1/60. Therefore, it will take 60 minutes to fill the tank.
Steps: 7
Step 1: Determine the rate at which the first pipe fills the tank. It fills the tank in 20 minutes, so its rate is 1 tank per 20 minutes, or 1/20 tanks per minute.
Step 2: Determine the rate at which the second pipe empties the tank. It empties the tank in 30 minutes, so its rate is 1 tank per 30 minutes, or 1/30 tanks 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: (1/20) - (1/30).
Step 4: To subtract these fractions, find a common denominator. The least common multiple of 20 and 30 is 60.
Step 5: Convert the rates to have the common denominator: (1/20) = (3/60) and (1/30) = (2/60).
Step 6: Now subtract the two rates: (3/60) - (2/60) = (1/60).
Step 7: The net rate of filling the tank is 1/60 tanks per minute, which means it takes 60 minutes to fill the tank when both pipes are open.
