SOLUTION: Working together, a man and a woman can do the job for 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

Question 903013: Working together, a man and a woman can do the job for 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?
Found 2 solutions by ewatrrr, richwmiller:
Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!
|Multiplying thru by 8x(x+2) so as all denominators = 1
8(x+2) + 8x = x(x+2)
x^2 -14x - 14 = 0 (Toss out the negative solution for unit measure)

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=252 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 14.9372539331938, -0.937253933193772. Here's your graph:

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:

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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