A tank can be filled by a pipe in 25 hours and emptied by another pipe in 50 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 25 hours and emptied by another pipe in 50 hours. If both pipes are opened together, how long will it take to fill the tank?
16.67 hours
20 hours
25 hours
30 hours
The net rate is 1/25 - 1/50 = 1/50. Therefore, it will take 50 hours to fill the tank.
Questions & Step-by-step Solutions
1 item
Q
Q: A tank can be filled by a pipe in 25 hours and emptied by another pipe in 50 hours. If both pipes are opened together, how long will it take to fill the tank?
Solution: The net rate is 1/25 - 1/50 = 1/50. Therefore, it will take 50 hours to fill the tank.
Steps: 8
Step 1: Determine the filling rate of the first pipe. It fills the tank in 25 hours, so its rate is 1/25 of the tank per hour.
Step 2: Determine the emptying rate of the second pipe. It empties the tank in 50 hours, so its rate is 1/50 of the 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: (1/25) - (1/50).
Step 4: To subtract the fractions, find a common denominator. The common denominator for 25 and 50 is 50.
Step 5: Convert 1/25 to have a denominator of 50: (1/25) = (2/50).
Step 6: Now subtract: (2/50) - (1/50) = (1/50).
Step 7: The net rate of filling the tank is 1/50 of the tank per hour.
Step 8: To find out how long it takes to fill the entire tank, take the reciprocal of the net rate: 1 / (1/50) = 50 hours.
