SOLUTION: Batman and Robin working together can capture the Joker in 3 hours. It takes Robin, working alone, 1 more hour than Batman to capture the Joker. Find how long it takes Robin to cap

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Question 241924: Batman and Robin working together can capture the Joker in 3 hours. It takes Robin, working alone, 1 more hour than Batman to capture the Joker. Find how long it takes Robin to capture the Joker working alone and how ling it takes Batman to capture the joker working alone.
Answer by nerdybill(7384) (Show Source):
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Batman and Robin working together can capture the Joker in 3 hours. It takes Robin, working alone, 1 more hour than Batman to capture the Joker. Find how long it takes Robin to capture the Joker working alone and how ling it takes Batman to capture the joker working alone.
.
Let x = hours it takes Batman to work alone
then
x+1 = hours it takes Robin to work alone
.
3(1/x + 1/(x+1)) = 1
3(x+1 + x) = x(x+1)
3(2x+1) = x(x+1)
6x+3 = x^2+x
0 = x^2+x-6x-3
0 = x^2-5x-3
Solving using the quadratic equation we get:
x = {5.5414, -0.5414}
We can toss out the neg answer leaving:
x = 5.5414 hours (time it takes Batman working alone)
.
Robin:
x+1 = 5.5414+1 = 6.5414 hours
.
Details of quadratic:

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=37 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 5.54138126514911, -0.54138126514911. Here's your graph: