A tank is filled by two pipes in 12 hours and 15 hours respectively. If the first pipe is opened for 5 hours and then the second pipe is opened, how long will it take to fill the tank completely?
Practice Questions
1 question
Q1
A tank is filled by two pipes in 12 hours and 15 hours respectively. If the first pipe is opened for 5 hours and then the second pipe is opened, how long will it take to fill the tank completely?
6 hours
7 hours
8 hours
9 hours
In 5 hours, the first pipe fills 5/12 of the tank. The remaining is 1 - 5/12 = 7/12. The combined rate of both pipes is 1/12 + 1/15 = 7/60. Therefore, it will take (7/12) / (7/60) = 60/12 = 5 hours to fill the remaining part.
Questions & Step-by-step Solutions
1 item
Q
Q: A tank is filled by two pipes in 12 hours and 15 hours respectively. If the first pipe is opened for 5 hours and then the second pipe is opened, how long will it take to fill the tank completely?
Solution: In 5 hours, the first pipe fills 5/12 of the tank. The remaining is 1 - 5/12 = 7/12. The combined rate of both pipes is 1/12 + 1/15 = 7/60. Therefore, it will take (7/12) / (7/60) = 60/12 = 5 hours to fill the remaining part.
Steps: 7
Step 1: Determine the rate at which each pipe fills the tank. The first pipe fills the tank in 12 hours, so its rate is 1/12 of the tank per hour. The second pipe fills the tank in 15 hours, so its rate is 1/15 of the tank per hour.
Step 2: Calculate how much of the tank the first pipe fills in 5 hours. Since the first pipe fills 1/12 of the tank in 1 hour, in 5 hours it fills 5/12 of the tank.
Step 3: Find out how much of the tank is left to fill after the first pipe has been running for 5 hours. The remaining part of the tank is 1 - 5/12 = 7/12.
Step 4: Calculate the combined rate of both pipes when they are both open. The combined rate is 1/12 + 1/15. To add these fractions, find a common denominator, which is 60. So, (5/60) + (4/60) = 9/60 = 3/20.
Step 5: Determine how long it will take to fill the remaining 7/12 of the tank with both pipes open. Use the formula: time = remaining part / combined rate. This gives us (7/12) / (3/20).
