SOLUTION: how do you solve a problem like this: One pipe can fill a reservoir 1 hr faster than another pipe. Together they can fill the reservoir in 4 hrs. How long to the nearest tenth of

Question 311523: how do you solve a problem like this:
One pipe can fill a reservoir 1 hr faster than another pipe. Together they can fill the reservoir in 4 hrs. How long to the nearest tenth of an hour does it take the faster pipe to fill the reservoir by itself?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
One pipe can fill a reservoir 1 hr faster than another pipe. Together they can fill the reservoir in 4 hrs. How long to the nearest tenth of an hour does it take the faster pipe to fill the reservoir by itself?
.
Let x = rate of slower pipe
then
x-1 = rate of faster pipe
.
4(1/x + 1/(x-1)) = 1
4((x-1) + x) = x(x-1)
4(2x-1) = x(x-1)
8x-4 = x^2-x
-4 = x^2-9x
0 = x^2-9x+4
Because we can't factor, we must resort to the quadratic formula. Doing so yields:
x = {0.5, 8.5}
Tossing out the 0.5 (because calculating the faster pipe will produce a negative answer) leaves:
x = 8.5 hrs
.
Time for faster pipe to fill: 8.5-1 = 7.5 hours
.
Details of quadratic follows:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=65 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 8.53112887414927, 0.468871125850725. Here's your graph:

RELATED QUESTIONS
umhh another problem sir, hehe I gone crazy just to solve this problem but still I can't... (answered by nerdybill)

ONE PIPE CAN FILL A POOL 1.25 TIMES FASTER THAN ANOTHER PIPE. WHEN BOTH PIPES ARE OPENED, (answered by Alan3354)

� One pipe can fill a tank in 5hrs less than another , together they fill the tank in... (answered by lwsshak3)

One pipe can fill a swimming pool in 6 hours, and another pipe can do it in 9 hr. How... (answered by josmiceli)

please help me solve this problem One pipe can fill a pool two and a half times faster... (answered by mananth)

PLEASE HELP! One pipe can fill a swimming pool in 5 hours less than another. Together... (answered by AnlytcPhil)

One pipe can fill a small reservoir in 15 hours, while with a second pipe also in... (answered by richwmiller)

One pipe can fill a storage tank in five hours less time than a smaller second pipe can,... (answered by ewatrrr,mananth)

"One pipe can fill a pool 1.25 times faster than a second pipe. When both pipes are... (answered by solver91311,Edwin McCravy)