A tank can be filled by a pipe in 12 hours and emptied by another pipe in 18 hours. 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 12 hours and emptied by another pipe in 18 hours. If both pipes are opened together, how long will it take to fill the tank?
10 hours
12 hours
15 hours
18 hours
The net rate is 1/12 - 1/18 = 1/36. Therefore, it will take 36 hours to fill the tank.
Questions & Step-by-step Solutions
1 item
Q
Q: A tank can be filled by a pipe in 12 hours and emptied by another pipe in 18 hours. If both pipes are opened together, how long will it take to fill the tank?
Solution: The net rate is 1/12 - 1/18 = 1/36. Therefore, it will take 36 hours 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 12 hours, so its rate is 1 tank per 12 hours, or 1/12 of the tank per hour.
Step 3: Determine the rate at which the emptying pipe works. It empties the tank in 18 hours, so its rate is 1 tank per 18 hours, or 1/18 of the tank per hour.
Step 4: Calculate the net rate when both pipes are open. This is done by subtracting the emptying rate from the filling rate: (1/12) - (1/18).
Step 5: To subtract these fractions, find a common denominator. The least common multiple of 12 and 18 is 36.
Step 6: Convert the rates to have the same denominator: (1/12) = (3/36) and (1/18) = (2/36).
Step 7: Now subtract the two rates: (3/36) - (2/36) = (1/36).
Step 8: The net rate of filling the tank is 1/36 of the tank per hour.
Step 9: To find out how long it takes to fill the entire tank, take the reciprocal of the net rate: 1 / (1/36) = 36 hours.
