SOLUTION: A tank can be filled by a pipe A in 3 hours and by pipe B in 5 hours. When the tank is full, it can be drained by pipe C in 4 hours. If the tank is initially empty and all three ar

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A tank can be filled by a pipe A in 3 hours and by pipe B in 5 hours. When the tank is full, it can be drained by pipe C in 4 hours. If the tank is initially empty and all three ar      Log On


   

Question 574428: A tank can be filled by a pipe A in 3 hours and by pipe B in 5 hours. When the tank is full, it can be drained by pipe C in 4 hours. If the tank is initially empty and all three are open, how many hours will it take to fill up the tank?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A tank can be filled by a pipe A in 3 hours and by pipe B in 5 hours.
When the tank is full, it can be drained by pipe C in 4 hours.
If the tank is initially empty and all three are open, how many hours will it take to fill up the tank?
:
let t = time to fill the tank when all pipes are open
Let the completed job (a full tank) = 1
+fill
-drain
:
Pipe A + Pipe B - Pipe C = Full Tank
t%2F3 + t%2F5 - t%2F4 = 1
Multiply by 60 to clear the denominators
60*t%2F3 + 60*t%2F5 - 60*t%2F4 = 60(1)
Cancel the denominators, you have
20t + 12t - 15t = 60
17t = 60
t = 60/17
t = 3.53 hrs with all pipes open
:
:
Check this using decimals
3.53%2F3 + 3.53%2F5 - 3.53%2F4 =
1.177 + .706 - .882 = 1.00 confirms our solutions of t = 3.53 hrs