SOLUTION: a small pipe takes 4 more hours to fill a pool than a larger pipe. the 2 pipes were opened at the same time to fill a pool with water. after 3 hours, the larger pipe was closed. it

Algebra ->  Rate-of-work-word-problems -> SOLUTION: a small pipe takes 4 more hours to fill a pool than a larger pipe. the 2 pipes were opened at the same time to fill a pool with water. after 3 hours, the larger pipe was closed. it      Log On


   

Question 478507: a small pipe takes 4 more hours to fill a pool than a larger pipe. the 2 pipes were opened at the same time to fill a pool with water. after 3 hours, the larger pipe was closed. it took 2 more hours for a smaller pipe to complete filling up the pool. How many hours will be needed for each pipe to fill the pool alone?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
a small pipe takes 4 more hours to fill a pool than a larger pipe.
the 2 pipes were opened at the same time to fill a pool with water.
after 3 hours, the larger pipe was closed. it took 2 more hours for a smaller pipe to complete filling up the pool.
How many hours will be needed for each pipe to fill the pool alone?
:
Let x = time required by the large pipe alone
then
(x+4) = time required by the small pipe
:
Let completed job = 1; (a full pool)
:
From the information given we know the large pipe was on for 3 hrs & the small pipe for 5 hrs
:
3%2Fx + 5%2F%28%28x%2B4%29%29 = 1
multiply each side x(x+4), results
3(x+4) + 5x = x(x+4)
3x + 12 + 5x = x^2 + 4x
8x + 12 = x^2 + 4x
0 = x^2 + 4x - 8x - 12
A quadratic equation
x^2 - 4x - 12 = 0
Factors to
(x-6)(x+2) = 0
The positive solution
x = 6 hrs for large pipe to fill the pool alone
then
6 + 4 = 10 hrs for the small pipe to do it
:
:
See if this adds up
3/6 + 5/10 = 1