SOLUTION: Pipe A can fill a pool in 5 hours. Pipe B can fill it in 2 hours less than it takes Pipe C, a drain pipe, to empty the pool. With all 3 pipes open it takes 3 hours to fill the po

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Pipe A can fill a pool in 5 hours. Pipe B can fill it in 2 hours less than it takes Pipe C, a drain pipe, to empty the pool. With all 3 pipes open it takes 3 hours to fill the po      Log On


   

Question 498554: Pipe A can fill a pool in 5 hours. Pipe B can fill it in 2 hours less than it takes Pipe C, a drain pipe, to empty the pool. With all 3 pipes open it takes 3 hours to fill the pool. How long would it take Pipe C to empty it?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
This is a problem of rates
Let c = pipe C's rate of emptying the pool
Pipe A's rate of filling:
+1%2F5+ ( 1 pool in 5 hrs )
Pipe B's rate of filling:
++1%2F%28+c+-+2%29+
Pipe C's rate of emptying pool:
c
----------
With all 3 pipes open:
+1%2F5+%2B+1%2F%28+c+-+2+%29+-+1%2Fc+=+1%2F3+
Multiply both sides by +15%2Ac%2A%28+c+-+2+%29+
+3c%2A%28+c+-+2+%29+%2B+15c+-+15%2A%28+c+-+2+%29+=+5c%2A%28+c+-+2+%29+
+3c%5E2+-+6c+%2B+15c+-+15c+%2B+30++=+5c%5E2+-+10c+
+2c%5E2+-+4c+-+30+=+0+
+c%5E2+-+2c+-+15+=+0+
Completing the square:
+c%5E2+-+2c+%2B+%28-2%2F2%29%5E2+=+15+%2B+%28-2%2F2%29%5E2+
+c%5E2+-+2c+%2B+1+=+16+
+%28+c+-+1+%29%5E2+=+4%5E2+
Take the square root of both sides
+c+-+1+=+4+
+c+=+5+
and, also
+c+-+1+=+-4+
+c+=+-3+ ( can't use the negative square root )
It will take pipe C alone 5 hours to empty pool
check answer:
+1%2F5+%2B+1%2F%28+c+-+2+%29+-+1%2Fc+=+1%2F3+
+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