Pipe A can fill a tank in 15 hours, and pipe B can fill the same tank in 20 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, and pipe B can fill the same tank in 20 hours. If both pipes are opened together, how long will it take to fill the tank?
6 hours
8 hours
10 hours
12 hours
The combined rate is 1/15 + 1/20 = 7/60. Therefore, it will take 60/7 hours, approximately 8.57 hours to fill the tank.
Questions & Step-by-step Solutions
1 item
Q
Q: Pipe A can fill a tank in 15 hours, and pipe B can fill the same tank in 20 hours. If both pipes are opened together, how long will it take to fill the tank?
Solution: The combined rate is 1/15 + 1/20 = 7/60. Therefore, it will take 60/7 hours, approximately 8.57 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 15 hours, its rate is 1 tank per 15 hours, or 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 20 hours, its rate is 1 tank per 20 hours, or 1/20 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 + 1/20.
Step 4: To add 1/15 and 1/20, find a common denominator. The least common multiple of 15 and 20 is 60.
Step 5: Convert 1/15 to a fraction with a denominator of 60. This is (1 * 4) / (15 * 4) = 4/60.
Step 6: Convert 1/20 to a fraction with a denominator of 60. This is (1 * 3) / (20 * 3) = 3/60.
Step 7: Now add the two fractions: 4/60 + 3/60 = 7/60.
Step 8: The combined rate of both pipes is 7/60 of the tank per hour.
Step 9: To find out how long it takes to fill the tank, take the reciprocal of the combined rate. This means you calculate 60/7 hours.
Step 10: Calculate 60/7, which is approximately 8.57 hours.
