A tank can be filled by a pipe in 40 minutes and emptied by another pipe in 60 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 40 minutes and emptied by another pipe in 60 minutes. If both pipes are opened together, how long will it take to fill the tank?
20 minutes
30 minutes
40 minutes
50 minutes
The net rate is 1/40 - 1/60 = 1/120. Therefore, it will take 120 minutes to fill the tank.
Questions & Step-by-step Solutions
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Q
Q: A tank can be filled by a pipe in 40 minutes and emptied by another pipe in 60 minutes. If both pipes are opened together, how long will it take to fill the tank?
Solution: The net rate is 1/40 - 1/60 = 1/120. Therefore, it will take 120 minutes to fill the tank.
Steps: 9
Step 1: Understand that one pipe fills the tank and the other pipe empties it.
Step 2: Determine the rate at which the filling pipe works. It fills the tank in 40 minutes, so its rate is 1 tank per 40 minutes, or 1/40 tanks per minute.
Step 3: Determine the rate at which the emptying pipe works. It empties the tank in 60 minutes, so its rate is 1 tank per 60 minutes, or 1/60 tanks per minute.
Step 4: Calculate the net rate when both pipes are open. This is done by subtracting the emptying rate from the filling rate: (1/40) - (1/60).
Step 5: To subtract these fractions, find a common denominator. The least common multiple of 40 and 60 is 120.
Step 6: Convert the rates to have the common denominator: (1/40) = (3/120) and (1/60) = (2/120).
Step 7: Now subtract the two rates: (3/120) - (2/120) = (1/120).
Step 8: The net rate of filling the tank is 1/120 tanks per minute.
Step 9: To find out how long it takes to fill 1 tank, take the reciprocal of the net rate: 1 / (1/120) = 120 minutes.
