Two pipes can fill a tank 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
Two pipes can fill a tank 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?
3 hours
4 hours
5 hours
6 hours
The first pipe fills 1/2 of the tank in 5 hours. The remaining half can be filled by both pipes in 2 hours.
Questions & Step-by-step Solutions
1 item
Q
Q: Two pipes can fill a tank 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 1/2 of the tank in 5 hours. The remaining half can be filled by both pipes 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 1/2 of the tank remaining.
Step 4: Calculate the combined rate of both pipes when they are both open. 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 two fractions: 1/10 + 1/15. The common denominator is 30, so (3/30) + (2/30) = 5/30 = 1/6. This means together they fill 1/6 of the tank in 1 hour.
Step 5: Determine how long it will take both pipes to fill the remaining 1/2 of the tank. Since they fill 1/6 of the tank in 1 hour, to fill 1/2 of the tank, we can set up the equation: (1/6) * t = 1/2. Solving for t gives t = (1/2) / (1/6) = (1/2) * (6/1) = 3 hours.
Step 6: Add the time the first pipe was open to the time it takes both pipes to fill the remaining tank. The first pipe was open for 5 hours, and it takes 3 more hours with both pipes, so the total time is 5 + 3 = 8 hours.
