SOLUTION: if one water pipe fills a swimming pool in x h. A second pipe takes 3h longer . The two pipes together fill the pool in 2h. How long will it take each pipe to fill the swimming poo

Algebra ->  Rate-of-work-word-problems -> SOLUTION: if one water pipe fills a swimming pool in x h. A second pipe takes 3h longer . The two pipes together fill the pool in 2h. How long will it take each pipe to fill the swimming poo      Log On


   

Question 732593: if one water pipe fills a swimming pool in x h. A second pipe takes 3h longer . The two pipes together fill the pool in 2h. How long will it take each pipe to fill the swimming pool separately?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The rate of filling for 1st pipe is:
( 1 pool filled / x hrs )
The rate of filling for 2nd pipe is:
( 1 pool filled / x + 3 hrs )
Add their rates of filling to get the
rate with both pipes open
+1%2Fx+%2B+1%2F%28+x%2B3+%29+=+1%2F2+
Multiply both sides by +2%2Ax%2A%28+x%2B3+%29+
+2%2A%28+x%2B3+%29+%2B+2x+=+x%2A%28+x%2B3+%29+
+2x+%2B+6+%2B+2x++=+x%5E2+%2B+3x+
+4x+%2B+6+=+x%5E2+%2B+3x+
+x%5E2+-+x+-+6+=+0+
Use quadratic formula
+x+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+-1+
+c+=+-6+
+x+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2+-+4%2A1%2A%28-6%29+%29%29+%2F+%282%2A1%29+
+x+=+%28+1+%2B-+sqrt%28+1+%2B+24%29%29+%2F+2+
+x+=+%28+1+%2B-+sqrt%28+25%29%29+%2F+2+
+x+=+%28+1+%2B+5+%29+%2F+2+ ( can't use negative sqrt )
+x+=+3+
+x+%2B+3+=+6+
The 1st pipe will take 3 hrs to fill pool
The 2nd pipe will take 6 hrs to fill pool
check:
+1%2Fx+%2B+1%2F%28+x%2B3+%29+=+1%2F2+
+1%2F3+%2B+1%2F%28+3%2B3+%29+=+1%2F2+
+1%2F3+%2B+1%2F6+=+1%2F2+
+2%2F6+%2B+1%2F6+=+3%2F6+
+3%2F6+=+3%2F6+
OK