Question 551349: ~Working together a man and woman can do the job in 8 hours. if either had to do it alone, it would take a woman 2 hours longer than a man. How long would it take either person working alone?
~A reservoir can be filled by one pipe in 6 hours and by another in 8 hours. It can be emptied by a third pipe in 10 hours. Starting empty, how long will it take to fill the reservoir if all pipes are open?
Found 2 solutions by mananth, richwmiller:
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! let Man take x hours to complete the job alone
so he does 1/x of the job in 1 hour
woman takes 1/(x+2) hours to do the same job
so she does 1/(x+2) of the job in 1 hour
Together they can do 1/x + 1/(x+2) of the job in 1 hour
add up both
=(2x+2)/x(x+2)
so they take x(x+2)/(2x+2) hours
x(x+2)/(2x+2)= 10
x(x+2)=10(2x+2)
x^2+2x=20x+20
x^2-18x-20=0
x^2-20x+2x-20=0
x(x-20)+2(x-20)=0
(x-20)(x+2)=0
Take the positive value
x= 20
Man takes 20 hours
Woman takes 20 +2 = 22 hours
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1/6 +1/8 - 1/10 is the job done in 1 hour ( filling the pool)
7/24 - 1/10
Addup
(70-24)/240
46/240 of the job is done in 1 hour
so it will take 240/46 hours = 5.2 hours
HAPPY NEW YEAR
Answer by richwmiller(17219)  (Show Source):
You can put this solution on YOUR website! 
Multiply by 8x(x+2) to remove denominators
8(x+2) + 8x = x(x+2)
x^2 -14x - 16 = 0
(Reject the negative solution for time)
| 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=260 is greater than zero. That means that there are two solutions:  .
Quadratic expression  can be factored:
Again, the answer is: 15.0622577482985, -1.06225774829855.
Here's your graph:
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| Solved by pluggable solver: COMPLETING THE SQUARE solver for quadratics |
Read this lesson on completing the square by prince_abubu, if you do not know how to complete the square.
Let's convert  to standard form by dividing both sides by 1:
We have: .
What we want to do now is to change this equation to a complete square  . How can we find out values of somenumber and othernumber that would make it work?
Look at  :  . Since the coefficient in our equation  that goes in front of x is -14, we know that -14=2*somenumber, or  . So, we know that our equation can be rewritten as  , and we do not yet know the other number.
We are almost there. Finding the other number is simply a matter of not making too many mistakes. We need to find 'other number' such that is equivalent to our original equation  .
The highlighted red part must be equal to -16 (highlighted green part).
 , or  .
So, the equation converts to  , or  .
Our equation converted to a square  , equated to a number (65).
Since the right part 65 is greater than zero, there are two solutions:
, or
Answer: x=15.0622577482985, -1.06225774829855.
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