SOLUTION: Pipe A can fill a tank in 2 hours and Pipe B can fill ii in half the it takes Pipe C to empty it. When all 3 are opened, it takes 1.5 hours to fill the pool. How much time is requi

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Pipe A can fill a tank in 2 hours and Pipe B can fill ii in half the it takes Pipe C to empty it. When all 3 are opened, it takes 1.5 hours to fill the pool. How much time is requi      Log On


   

Question 143381This question is from textbook algebra: structure and method: book1
: Pipe A can fill a tank in 2 hours and Pipe B can fill ii in half the it takes Pipe C to empty it. When all 3 are opened, it takes 1.5 hours to fill the pool. How much time is required for Pipe C to empty the tank? PLEASE HELP! The answer is 6 hours, but I don't know how to get there. HELP MUCH APPRECIATED!! This question is from textbook algebra: structure and method: book1

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Pipe A can fill a tank in 2 hours and Pipe B can fill it in half the time it takes
Pipe C to empty it. When all 3 are opened, it takes 1.5 hours to fill the pool.
How much time is required for Pipe C to empty the tank?
:
Let t = time required for Pipe C to empty the tank:
:
It says, "Pipe B can fill it in half the time it takes Pipe C to empty it."
therefore:
Let .5t = time for Pipe B to fill the tank
:
Let the full pool = 1
:
Filling is positive, emptying is negative:
:
1.5%2F2 + 1.5%2F.5t - 1.5%2Ft = 1
Multiply equation 2t, to get rid of the denominators:
1.5t + 1.5(4) - 1.5(2) = 2t(1)
:
1.5t + 6 - 3 = 2t
:
1.5t - 2t = +3 - 6
:
-.5t = -3
t = %28-3%29%2F%28-.5%29
t = +6 hrs for the pipe to empty a full pool
:
:
Check solution using original equation:
1.5%2F2 + 1.5%2F3 - 1.5%2F6 =
.75 + .5 - .25 = 1; confirms our solution