A tank is filled by two pipes in 10 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?
Practice Questions
1 question
Q1
A tank is filled by two pipes in 10 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?
2 hours
3 hours
4 hours
5 hours
The first pipe fills 1/10 * 5 = 1/2 of the tank. The remaining 1/2 can be filled by both pipes together in 2 hours.
Questions & Step-by-step Solutions
1 item
Q
Q: A tank is filled by two pipes in 10 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?
Solution: The first pipe fills 1/10 * 5 = 1/2 of the tank. The remaining 1/2 can be filled by both pipes together in 2 hours.
Steps: 6
Step 1: Determine the rate at which each pipe fills the tank. The first pipe fills the tank in 10 hours, so it fills 1/10 of the tank in 1 hour. The second pipe fills the tank in 15 hours, so it fills 1/15 of the tank in 1 hour.
Step 2: Calculate how much of the tank the first pipe fills in 5 hours. Since it fills 1/10 of the tank in 1 hour, in 5 hours it fills 5 * (1/10) = 5/10 = 1/2 of the tank.
Step 3: Determine how much of the tank is left to fill after the first pipe has been running for 5 hours. Since the first pipe filled 1/2 of the tank, there is 1 - 1/2 = 1/2 of the tank remaining to be filled.
Step 4: Calculate the combined rate of both pipes when they are opened together. The first pipe fills 1/10 of the tank in 1 hour and the second pipe fills 1/15 of the tank in 1 hour. To find their combined rate, add these fractions: 1/10 + 1/15. The common denominator is 30, so (3/30) + (2/30) = 5/30 = 1/6 of the tank per hour.
Step 5: Determine how long it will take both pipes to fill the remaining 1/2 of the tank together. Since they fill 1/6 of the tank in 1 hour, to fill 1/2 of the tank, it will take (1/2) / (1/6) = (1/2) * (6/1) = 3 hours.
Step 6: Add the time the first pipe was open (5 hours) to the time it takes both pipes to fill the remaining tank (3 hours). So, the total time to fill the tank is 5 + 3 = 8 hours.
