SOLUTION: Pipe A can fill a tank in five hours pipe B can fill it in two hours less than it takes pipe C, a drain pipe ,to empty the tank. with all three pipes open it takes three hours to f

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Question 1129779: Pipe A can fill a tank in five hours pipe B can fill it in two hours less than it takes pipe C, a drain pipe ,to empty the tank. with all three pipes open it takes three hours to fill the tank. how long would it take pipe C to empty it?
Found 3 solutions by josgarithmetic, josmiceli, ikleyn:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
c, the time for pipe C to drain the tank if pipe C is working alone
c-2, time for pipe B to fill the tank if working alone

1%2F5%2B1%2F%28c-2%29-1%2Fc=1%2F3
.
.
c%5E2-2c=15


highlight%28c=5%29

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Pipe A's rate of filling:
[ 1 tank filled ] / [ 5 hrs ]
Let +t+ = time in hrs for pipe C to empty tank
pipe C's rate of emptying:
[ 1 tank emptied ] / [ t hrs ]
pipe B's rate of filling:
[ 1 take filled ] / [ t - 2 hrs ]
---------------------------------
Add rates for A % B
Subtract rate for C
+1%2F5+%2B+1%2F%28+t-2+%29+-+1%2Ft+=+1%2F3+
Multiply both sides by +3%2A5%2At%2A%28+t-2+%29+
+3t%2A%28+t-2+%29+%2B+3%2A5t+-+3%2A5%2A%28+t-2+%29+=+5t%2A%28+t-2+%29+
+3t%5E2+-+6t+%2B+15t+-+15t+%2B+30+=+5t%5E2+-+10t+
+3t%5E2+-+6t+%2B+30+=+5t%5E2+-+10t+
+2t%5E2+-+4t+-+30+=+0+
+t%5E2+-+2t+-+15+=+0+
+%28+t+-+5+%29%2A%28+t+%2B+3+%29+=+0+
+t+=+5+ ( choose positive time )
Pipe C empties the tank in 5 hrs
--------------------------------------
check:
+1%2F5+%2B+1%2F%28+5-2%29+-+1%2F5+=+1%2F3+
+1%2F5+%2B+1%2F3+-+1%2F5+=+1%2F3+
+1%2F3+=+1%2F3+
OK

Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let x be the time for pipe C to empty the tank.


Then the time for the pipe B to fill the tank is (x+2) hours.


The rate of work for pipes A, B and C are  1%2F5,  1%2F%28x-2%29 and  -1%2Fx of the tank volume per hour.


The balance equation is


    1%2F5 + 1%2F%28x-2%29 - 1%2Fx = 1%2F3,    or

    1%2F%28x-2%29 - 1%2Fx = 1%2F3+-+1%2F5 = 5%2F15-3%2F15 = 2%2F15.


To solve it, multiply both sides by  15*x*(x-2)  and simplify step by step.  You will get


    15x - 15*(x-2) = 2x*(x-2)

    30 = 2x^2 - 4x

    2x^2 - 4x - 30 = 0

    x^2 - 2x - 15 = 0

    (x-5)*(x+3) = 0


Answer.  x = 5 hours.


Check.  1%2F5 + 1%2F%285-2%29 - 1%2F5 = 1%2F3  of the tank volume.   ! Correct !

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To see many other similar solved problems,  look into the lessons
    - Using Fractions to solve word problems on joint work
    - Solving more complicated word problems on joint work
    - Selected joint-work word problems from the archive


Read them and get be trained in solving joint-work problems.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic
"Rate of work and joint work problems"  of the section  "Word problems".


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Free of charge online textbook in ALGEBRA-I
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