Pipe A can fill a tank in 6 hours, and pipe B can fill the same tank in 9 hours. If both pipes are opened together, how long will it take to fill the tank?
Practice Questions
1 question
Q1
Pipe A can fill a tank in 6 hours, and pipe B can fill the same tank in 9 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 combined rate is 1/6 + 1/9 = 5/18. Therefore, it will take 18/5 = 3.6 hours to fill the tank.
Questions & Step-by-step Solutions
1 item
Q
Q: Pipe A can fill a tank in 6 hours, and pipe B can fill the same tank in 9 hours. If both pipes are opened together, how long will it take to fill the tank?
Solution: The combined rate is 1/6 + 1/9 = 5/18. Therefore, it will take 18/5 = 3.6 hours to fill the tank.
Steps: 10
Step 1: Determine the rate at which Pipe A fills the tank. Since Pipe A can fill the tank in 6 hours, its rate is 1 tank per 6 hours, or 1/6 of the tank per hour.
Step 2: Determine the rate at which Pipe B fills the tank. Since Pipe B can fill the tank in 9 hours, its rate is 1 tank per 9 hours, or 1/9 of the tank per hour.
Step 3: Add the rates of both pipes together to find the combined rate. This is done by calculating 1/6 + 1/9.
Step 4: To add 1/6 and 1/9, find a common denominator. The least common multiple of 6 and 9 is 18.
Step 5: Convert 1/6 to have a denominator of 18: (1/6) * (3/3) = 3/18.
Step 6: Convert 1/9 to have a denominator of 18: (1/9) * (2/2) = 2/18.
Step 7: Now add the two fractions: 3/18 + 2/18 = 5/18.
Step 8: The combined rate of both pipes is 5/18 of the tank per hour.
Step 9: To find out how long it takes to fill the entire tank, take the reciprocal of the combined rate: 1 / (5/18) = 18/5 hours.
