SOLUTION: Pipe A can fill a tank in 4h. Pipe B can fill the tank in 9 h less than the time it takes pipe C, a drain pipe, to empty the tank. When all 3 pipes are open, it takes 2h to fill th

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Pipe A can fill a tank in 4h. Pipe B can fill the tank in 9 h less than the time it takes pipe C, a drain pipe, to empty the tank. When all 3 pipes are open, it takes 2h to fill th      Log On


   

Question 339103: Pipe A can fill a tank in 4h. Pipe B can fill the tank in 9 h less than the time it takes pipe C, a drain pipe, to empty the tank. When all 3 pipes are open, it takes 2h to fill the tank. How much time is required for pipe c to empty the tank if pipes A and B are closed.
thank you for your help!
Answer by jrfrunner(365) About Me  (Show Source):
You can put this solution on YOUR website!
Given
Pipe A fills tank in 4 hours
Pipe C empties tank in C hours
Pipe B fills tank in C-9 hours
--
this means that every hour
Pipe A filles 1/4 of tank
Pipe C empties 1/c of tank
Pipe B fills 1/(c-9) of tank
--
When all pipes are open (ie working together) they fill the tank in 2 hours
soo.....
"every hour", working together 1/2 the tank is filled.
Pipe A + pipe B -Pipe C =%281%2F4%29%2B1%2F%28c-9%29-1%2Fc=1%2F2 solve for c
--
1%2F%28c-9%29-1%2Fc=1%2F2-1%2F4=1%2F4 subtract 1/4 from both sides
c%2F%28c%2A%28c-9%29%29-%28c-9%29%2F%28%28c-9%29%2Ac%29=1%2F4 get common denominator
%28c-%28c-9%29%29%2F%28c%2A%28c-9%29%29=1%2F4
9%2F%28c%5E2-9%2Ac%29=1%2F4 combine and distribute terms
36=c%5E2-9c
0=c%5E2-9%2Ac-36
---
factor
0=(c-12)*(c+3)
so c=12, or c=-3, since solution must be positive c=-3 is extraneous
answer: c=12
--
You could use use quadratic solution, a=1,b=-9, c=-36
c=%289%2Bsqrt%28%28-9%29%5E2-4%2A1%2A%28-36%29%29%29%2F%282%2A1%29 or c=%289-sqrt%28%28-9%29%5E2-4%2A1%2A%28-36%29%29%29%2F%282%2A1%29