If a tank can be filled by a pipe in 20 minutes and emptied by another pipe 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 tank can be filled by a pipe in 20 minutes and emptied by another pipe 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 tank can be filled by a pipe in 20 minutes and emptied by another pipe 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 filling pipe works. If it fills the tank in 20 minutes, its rate is 1 tank per 20 minutes, or 1/20 tanks per minute.
Step 2: Determine the rate at which the emptying pipe works. If it empties the tank in 30 minutes, 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). This means the net rate is 1/60 tanks per minute.
Step 7: To find out how long it takes to fill the tank at this net rate, take the reciprocal of the net rate: 1 / (1/60) = 60 minutes.
