SOLUTION: I have this problem from school and i need to get this done. I have tried toyed around with this problem for 1 hour and don't seem to get anywhere. I have tried to replace variabl

Algebra ->  Rate-of-work-word-problems -> SOLUTION: I have this problem from school and i need to get this done. I have tried toyed around with this problem for 1 hour and don't seem to get anywhere. I have tried to replace variabl      Log On


   

Question 498679: I have this problem from school and i need to get this done. I have tried toyed around with this problem for 1 hour and don't seem to get anywhere. I have tried to replace variables and tried the quadratic formula but nothing seems to work. If you could help that would be amazing.

Pipe A can fill a tank in 6 hours, and pipe B can fill it in 2 hours less time than it take drain pipe C to empty the tank. With all three pipes open it takes 3 hours 20 minutes to fill the tank. How long would it take pipe C to empty it???????
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Pipe A can fill a tank in 6 hours, and pipe B can fill it in 2 hours less time than it take drain pipe C to empty the tank. With all three pipes open it takes 3 hours 20 minutes to fill the tank. How long would it take pipe C to empty it
Make this chart:

               Number of     Time to      Rate in
              tanks filled    fill       tanks/hours
Pipe A
Pipe B
Drain C
All three

The number of tanks filled is 1 for each of those except Drain C, and
we put -1 for the number of tanks it filled. We can fill in the times
for C and All three from the problem, and we get this:



               Number of     Time to      Rate in
              tanks filled    fill       tanks/hours
Pipe A            1            6  
Pipe B            1           
Drain C          -1            
All three         1           3 1/3


Let the time for C to drain be x.  Then B's time to fill is x-2.
Fill those in:

               Number of     Time to      Rate in
              tanks filled    fill       tanks/hours
Pipe A            1            6           
Pipe B            1           x-2         
Drain C          -1            x           
All three         1          3 1/3


Fill in the rates in tanks/hour by dividing the number of
tanks filled by the number of hours:
         

               Number of     Time to      Rate in
              tanks filled    fill       tanks/hours
Pipe A            1            6            1/6
Pipe B            1           x-2          1/(x-2)
Drain C          -1            x           -1/x
All three         1          3 1/3          1%2F%283%261%2F3%29




1%2F6%2B1%2F%28x-2%29-1%2Fx=1%2F%283%261%2F3%29

First we simplify the last term: 1%2F%283%261%2F3%29=1%2F%2810%2F3%29=1%2Aexpr%283%2F10%29=3%2F10

1%2F6%2B1%2F%28x-2%29-1%2Fx=3%2F10%29

The LCD is 30x(x-2) so multiply through by that:

5x%28x-2%29%2B30x-30%28x-2%29=9x%28x-2%29

5x%5E2-10x%2B30x-30x%2B60=9x%5E2-18x

5x%5E2-10x%2B60=9x%5E2-18x

0=4x%5E2%2B8x-60

0=x%5E2-2x-15

%28x-5%29%28x%2B3%29=0

x-5=0,  x%2B3=0
x=5     x=-3

Discard the negative time.

It would take drain C 5 hours to empty the tank. 

Edwin