SOLUTION: Lee can frame a cabin in 4 days less than Ron. When they work together, they will do the job in 4 days. How long would each of them take to frame the cabin alone?

Question 312525: Lee can frame a cabin in 4 days less than Ron. When they work together, they will do the job in 4 days. How long would each of them take to frame the cabin alone?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Lee can frame a cabin in 4 days less than Ron. When they work together, they will do the job in 4 days. How long would each of them take to frame the cabin alone?
.
Let x = days it taks Ron to frame it alone
then
x-4 = days it takes Lee to frame it alone
.
4(1/x + 1/(x-4)) = 1
multiplying both sides by x(x-4):
4((x-4) + x) = x(x-4)
4(2x-4) = x(x-4)
8x-8 = x^2-4x
-8 = x^2-12x
0 = x^2-12x+8
x = {11.292, 0.708}
Tossing out the 0.708 (because it won't make sense) leaves us with:
x = 11.292 days (Time it takes Ron)
.
Lee:
x-4 = 11.292-4 = 7.292 days
.

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=112 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 11.2915026221292, 0.708497377870819. Here's your graph:

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