If a pipe can fill a tank in 9 hours and another pipe can fill it in 6 hours, how long will it take to fill the tank if both pipes are opened together?
Practice Questions
1 question
Q1
If a pipe can fill a tank in 9 hours and another pipe can fill it in 6 hours, how long will it take to fill the tank if both pipes are opened together?
3.6 hours
4 hours
4.5 hours
5 hours
The combined rate is 1/9 + 1/6 = 5/18. Therefore, it will take 18/5 = 3.6 hours to fill the tank.
Questions & Step-by-step Solutions
1 item
Q
Q: If a pipe can fill a tank in 9 hours and another pipe can fill it in 6 hours, how long will it take to fill the tank if both pipes are opened together?
Solution: The combined rate is 1/9 + 1/6 = 5/18. Therefore, it will take 18/5 = 3.6 hours to fill the tank.
Steps: 9
Step 1: Determine the rate at which each pipe fills the tank. The first pipe fills the tank in 9 hours, so its rate is 1/9 of the tank per hour.
Step 2: The second pipe fills the tank in 6 hours, so its rate is 1/6 of the tank per hour.
Step 3: Add the rates of both pipes together to find the combined rate. This is 1/9 + 1/6.
Step 4: To add 1/9 and 1/6, find a common denominator. The least common multiple of 9 and 6 is 18.
Step 5: Convert 1/9 to 2/18 and 1/6 to 3/18.
Step 6: Now add the two fractions: 2/18 + 3/18 = 5/18.
Step 7: The combined rate of both pipes is 5/18 of the tank per hour.
Step 8: 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.
