A tank can be filled by a pipe in 5 hours and emptied by another pipe in 10 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 5 hours and emptied by another pipe in 10 hours. If both pipes are opened together, how long will it take to fill the tank?
3 hours
4 hours
5 hours
6 hours
The net rate is 1/5 - 1/10 = 1/10. Therefore, it will take 10 hours to fill the tank.
Questions & Step-by-step Solutions
1 item
Q
Q: A tank can be filled by a pipe in 5 hours and emptied by another pipe in 10 hours. If both pipes are opened together, how long will it take to fill the tank?
Solution: The net rate is 1/5 - 1/10 = 1/10. Therefore, it will take 10 hours to fill the tank.
Steps: 5
Step 1: Determine the filling rate of the first pipe. It fills the tank in 5 hours, so its rate is 1 tank per 5 hours, or 1/5 of the tank per hour.
Step 2: Determine the emptying rate of the second pipe. It empties the tank in 10 hours, so its rate is 1 tank per 10 hours, or 1/10 of the tank per hour.
Step 3: Calculate the net rate when both pipes are opened together. Subtract the emptying rate from the filling rate: (1/5) - (1/10).
Step 4: To subtract the fractions, find a common denominator. The common denominator for 5 and 10 is 10. Convert 1/5 to 2/10. Now, subtract: 2/10 - 1/10 = 1/10.
Step 5: The net rate of filling the tank is 1/10 of the tank per hour. This means it takes 10 hours to fill the entire tank.
