SOLUTION: Two mechanics, Bonita Rich and Pamela Pearson, take 8 hours to re-build an engine when they work together. If each worked alone, Bonita, the more experienced mechanic could comple

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Question 134366: Two mechanics, Bonita Rich and Pamela Pearson, take 8 hours to re-build an engine when they work together. If each worked alone, Bonita, the more experienced mechanic could complete the job 2 hours faster than Pamela. How long would it take each of them to re-build the engine working alone?
The time it takes Bonita is about ? hours. Round to two decimal places as needed.
The time it takes Pamela is about ? hours. Round to two decimal places as needed.
Answer by edjones(8007) (Show Source):
You can put this solution on YOUR website!
Let b=Bonita's time working alone, b+2=Pamela's time working alone.
Bonita can do 1/b of the job in 1 hr.
Pamela can do 1/(b+2) of the job in 1 hr.
Together they do 1/8 of the job in 1 hr.
1/b + 1/(b+2) = 1/8 LCD=8b(b+2)
8(b+2)+8b=b(b+2) multiply each side by the LCD to eliminate fractions.
8b+16+8b=b^2+2b
b^2+2b-8b-16-8b=0
b^2-14b-16=0
b=15.06 hrs.
b+2=17.06 hrs.
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Ed
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

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: