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

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) (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
:
+ = 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
RELATED QUESTIONS
Word Problem: A small pipe takes 4 more hour to fill a pool than a larger pipe. The two... (answered by josgarithmetic)

Two pipes can be used to fill a pool. Working together, the two pipes can fill the pool... (answered by stanbon)

Three water pipes are used to fill a swimming pool. The first pipe alone takes 4 hours to (answered by lwsshak3)

Two pipes can be used to fill a pool. Working together the two pipes can fill the pool... (answered by ankor@dixie-net.com)

Two pipes can be used to fill a pool. Working together, the two pipes can fill... (answered by josgarithmetic,mananth)

A small pipe can fill a tank in 8 min more time than it takes a larger pipe to fill the... (answered by ikleyn)

Pipe A can fill a pool in 8 hours, while Pipe b can fill the same pool in 4 hours. Find... (answered by solver91311)

In a water refilling station, the time that a pipe takes to fill a tank is 10 minutes... (answered by josgarithmetic)