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?
:
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/3}}} + {{{t/5}}} - {{{t/4}}} = 1
Multiply by 60 to clear the denominators
60*{{{t/3}}} + 60*{{{t/5}}} - 60*{{{t/4}}} = 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
{{{3.53/3}}} + {{{3.53/5}}} - {{{3.53/4}}} = 
1.177 + .706 - .882 = 1.00 confirms our solutions of t = 3.53 hrs