A tank is filled by two pipes A and B in 15 hours and 25 hours respectively. If both pipes are opened together, how long will it take to fill the tank?
Practice Questions
1 question
Q1
A tank is filled by two pipes A and B in 15 hours and 25 hours respectively. If both pipes are opened together, how long will it take to fill the tank?
9 hours
10 hours
12 hours
15 hours
The combined rate is 1/15 + 1/25 = 2/15. Therefore, it will take 15/2 = 7.5 hours to fill the tank.
Questions & Step-by-step Solutions
1 item
Q
Q: A tank is filled by two pipes A and B in 15 hours and 25 hours respectively. If both pipes are opened together, how long will it take to fill the tank?
Solution: The combined rate is 1/15 + 1/25 = 2/15. Therefore, it will take 15/2 = 7.5 hours to fill the tank.
Steps: 10
Step 1: Determine the rate at which pipe A fills the tank. Since it fills 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 it fills the tank in 25 hours, its rate is 1/25 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 + 1/25.
Step 4: To add the fractions, find a common denominator. The least common multiple of 15 and 25 is 75.
Step 5: Convert 1/15 to have a denominator of 75: (1/15) * (5/5) = 5/75.
Step 6: Convert 1/25 to have a denominator of 75: (1/25) * (3/3) = 3/75.
Step 7: Now add the two fractions: 5/75 + 3/75 = 8/75.
Step 8: The combined rate of both pipes is 8/75 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: 1 / (8/75) = 75/8 hours.
Step 10: Simplify 75/8 to get the time in hours: 75/8 = 9.375 hours, which is 9 hours and 22.5 minutes.
