Pipe A can fill a tank in 15 hours, while pipe B can fill it in 10 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 15 hours, while pipe B can fill it in 10 hours. If both pipes are opened together, how long will it take to fill the tank?
4 hours
5 hours
6 hours
7 hours
The combined rate is 1/15 + 1/10 = 1/6. Therefore, it will take 6 hours to fill the tank.
Questions & Step-by-step Solutions
1 item
Q
Q: Pipe A can fill a tank in 15 hours, while pipe B can fill it in 10 hours. If both pipes are opened together, how long will it take to fill the tank?
Solution: The combined rate is 1/15 + 1/10 = 1/6. Therefore, it will take 6 hours to fill the tank.
Steps: 8
Step 1: Determine the rate at which Pipe A fills the tank. Since Pipe A can fill the tank in 15 hours, its rate is 1/15 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 10 hours, its rate is 1/10 of the tank per hour.
Step 3: Add the rates of both pipes together to find the combined rate. This is done by calculating 1/15 + 1/10.
Step 4: To add 1/15 and 1/10, find a common denominator. The least common multiple of 15 and 10 is 30.
Step 5: Convert 1/15 to 2/30 and 1/10 to 3/30.
Step 6: Now add the two fractions: 2/30 + 3/30 = 5/30.
Step 7: Simplify 5/30 to 1/6. This means together, both pipes can fill 1/6 of the tank in one hour.
Step 8: To find out how long it takes to fill the entire tank, take the reciprocal of 1/6, which is 6 hours.
