Three pipes can fill the tank in 18 hours. One of the pipes can fill it in 9…
2023
Three pipes can fill the tank in 18 hours. One of the pipes can fill it in 9 hours and the other can empty in 12 hours. At what rate does the third pipe work ?
- A.
Filling the tank in 18 hours
- B.
Waste pipe emptying the tank in 27 hours.
- C.
Filling the tank in 36 hours
- D.
Waste pipe emptying the tank in 18 hours
Attempted by 11 students.
Show answer & explanation
Correct answer: C
Solution:
Let x be the time (in hours) the third pipe takes to fill the tank.
Rates: first pipe fills at 1/9 tank per hour, the waste pipe empties at 1/12 tank per hour (so use -1/12), and the third pipe fills at 1/x.
The combined rate of the three pipes is given as 1/18 tank per hour, so:
1/9 - 1/12 + 1/x = 1/18
Compute 1/9 - 1/12 = 1/36, so 1/36 + 1/x = 1/18.
Then 1/x = 1/18 - 1/36 = 1/36, so x = 36 hours.
Answer: The third pipe fills the tank in 36 hours.