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

Question 143414This 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 ptaylor(2198) (Show Source): You can put this solution on YOUR website!

YOU ARE CORRECT!!! THE ANSWER IS SIX HOURS.
Let t=time required for Pipe C to empty the tank
Pipe C empties the tank at the rate of 1/t tank per hour
Pipe A fills at the rate of 1/2 tank per hour
Pipe B fills tha tank in t/2 hours, so
Pipe B fills at the rate of 2/t tank per hour
When all three pipes are open they fill at the rate of 1/1.5 tank per hour. So our equation to solve is:
1/2+2/t-1/t=1/1.5 simplify
1/2+1/t=1/1.5 multiply each term by 6t
3t+6=4t subtract 3t from each side
3t-3t+6=4t-3t collect like terms
6=t or
t=6 hours------------------time required for Pipe C to empty the tank
CK
1/2+1/6=1/1.5
3/6+1/6=1/1.5
4/6=1/1.5
1/1.5=1/1.5

Hope this helps---ptaylor

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