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