If pipe A can fill a tank in 10 hours and pipe B can fill it in 15 hours, how long will it take to fill the tank if both pipes are opened together?
Practice Questions
1 question
Q1
If pipe A can fill a tank in 10 hours and pipe B can fill it in 15 hours, how long will it take to fill the tank if both pipes are opened together?
4 hours
5 hours
6 hours
7 hours
The combined rate is 1/10 + 1/15 = 1/6. Therefore, it will take 6 hours to fill the tank.
Questions & Step-by-step Solutions
1 item
Q
Q: If pipe A can fill a tank in 10 hours and pipe B can fill it in 15 hours, how long will it take to fill the tank if both pipes are opened together?
Solution: The combined rate is 1/10 + 1/15 = 1/6. Therefore, it will take 6 hours to fill the tank.
Steps: 9
Step 1: Determine the rate at which pipe A fills the tank. Since it can fill the tank in 10 hours, its rate is 1 tank per 10 hours, or 1/10 of the tank per hour.
Step 2: Determine the rate at which pipe B fills the tank. Since it can fill the tank in 15 hours, its rate is 1 tank per 15 hours, or 1/15 of the tank per hour.
Step 3: Add the rates of both pipes together to find the combined rate. This is done by calculating 1/10 + 1/15.
Step 4: To add 1/10 and 1/15, find a common denominator. The least common multiple of 10 and 15 is 30.
Step 5: Convert 1/10 to a fraction with a denominator of 30. This is 3/30.
Step 6: Convert 1/15 to a fraction with a denominator of 30. This is 2/30.
Step 7: Now add the two fractions: 3/30 + 2/30 = 5/30.
Step 8: Simplify 5/30 to 1/6. This means together, both pipes can fill 1/6 of the tank in one hour.
Step 9: To find out how long it takes to fill the entire tank, take the reciprocal of 1/6. This gives you 6 hours.
