SOLUTION: A swimming pool is filled with water by using two taps A and B. Alone, it takes tap A 3 hours less than B to fill the same pool. Together, taps A and B take 2 hours to fill the poo

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A swimming pool is filled with water by using two taps A and B. Alone, it takes tap A 3 hours less than B to fill the same pool. Together, taps A and B take 2 hours to fill the poo      Log On


   

Question 755004: A swimming pool is filled with water by using two taps A and B. Alone, it takes tap A 3 hours less than B to fill the same pool. Together, taps A and B take 2 hours to fill the pool. How many hours does it take each tap to fill the swimming pools seperately?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their separate rates to get their rate filling together
B's rate of filling:
( 1 pool filled ) / ( t hrs )
A's rate of filling:
( 1 pool filled ) / ( t - 3 hrs )
A and B together:
( 1 pool filled ) / ( 2 hrs )
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+1%2F%28+t+-+3+%29+%2B+1%2Ft+=+1%2F2+
Multiply both sides by +t%2A%28+t-3+%29%2A2+
+2t+%2B+2%2A%28+t-3+%29+=+t%2A%28+t-3+%29+
+2t+%2B+2t+-+6+=+t%5E2+-+3t+
+4t+-+6+=+t%5E2+-+3t+
+t%5E2+-+7t+%2B+6+=+0+
+%28+t+-+6+%29%2A%28+t+-+1+%29+=+0+ ( by inspection )
+t+=+6+ ( note that +t=1+ doesn't work )
+t+-+3+=+3+
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A takes 3 hrs to fill the pool alone
B takes 6 hrs to fill the pool alone
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check:
+1%2F%28+t+-+3+%29+%2B+1%2Ft+=+1%2F2+
+1%2F3+%2B+1%2F6+=+1%2F2+
+2%2F6+%2B+1%2F6+=+3%2F6+
+3%2F6+=+3%2F6+
OK