SOLUTION: One water pipe fills a water tank in x hours. A second pipe takes 3 hours longer. The two pipes together fill the water tank in 2 hours. How long would it take each pipe to fill

Algebra ->  Rate-of-work-word-problems -> SOLUTION: One water pipe fills a water tank in x hours. A second pipe takes 3 hours longer. The two pipes together fill the water tank in 2 hours. How long would it take each pipe to fill       Log On


   

Question 898080: One water pipe fills a water tank in x hours. A second pipe takes 3 hours longer. The two pipes
together fill the water tank in 2 hours. How long would it take each pipe to fill the water tank
separately?

Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
The rates for each pipe:
1/x
1/(x+3)
Both at same time:
.

Both together do the job in 2 hours.
highlight_green%28%282x%2B3%29%2F%28x%28x%2B3%29%29=1%2F2%29
2x%2B3=%28x%5E2%2B3x%29%2F2
2%282x%2B3%29=x%5E2%2B3x
4x%2B6=x%5E2%2B3x
x%2B6=x%5E2
x%5E2-x-6=0
%28x%2B2%29%28x-3%29=0

The solution which makes sense is highlight%28highlight%28x=3%29%29.
First pipe would take 3 hours;
Second pipe alone would take 6 hours.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of filling to get their
rate filling together
1st pipe's rate:
( 1 tank ) / ( x hrs )
2nd pipe's rate:
( 1 tank ) / ( x + 3 hrs )
Rate with both pipes filling:
( 1 tank ) / ( 2 hrs )
----------------------------
+1%2Fx+%2B+1%2F%28+x+%2B+3+%29+=+1%2F2+
Multiply both sides by +x%2A%28+x+%2B+3+%29%2A2+
+2%2A%28+x%2B3+%29+%2B+2x+=+x%2A%28+x%2B3+%29+
+2x+%2B+6+%2B+2x+=+x%5E2+%2B+3x+
+x%5E2+-+x+-+6+=+0+
+%28+x+-+3+%29%2A%28+x+%2B+2+%29+=+0+ ( by inspection )
+x+=+3+ is the positive answer, so
+x+%2B+3+=+6+
-----------------
The 1st pipe takes 3 hrs
The 2nd pipe takes 6 hrs
----------------------
check:
+1%2Fx+%2B+1%2F%28+x+%2B+3+%29+=+1%2F2+
+1%2F3+%2B+1%2F6+=+1%2F2+
+2%2F6+%2B+1%2F6+=+3%2F6+
+3%2F6+=+3%2F6+
OK