Question 1102180: Two mechanics, Bonita Rich and Pamela Pearson, take 5 hours to rebuild an engine when they work together. If each worked alone, Bonita, the more experienced mechanic, could complete the job 3 hours faster than Pamela. How long would it take each of them to rebuild the engine working alone?
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! 1/x+1/(x+3)=1/5
(5*x*(x+3))/x+(5*x*(x+3))/(x+3)=(5*x*(x+3))/5
(5*(x+3))+5*x=x*(x+3)
5*x+15+5*x=x^2+3*x
10*x+15=x^2+3*x
x^2-7*x-15=0
Can it be factored?
What factors of -15 add up to -7?
Nevertheless, we will complete the square
x^2-7*x=15
Add it.
x^2-7*x+(-7/2)=15+(-7/2)
Square it.
x^2-7*x+(49/4)=15+(49/4)
x^2-7*x+(12.25)=15+(12.25)
x^2-7*x+(12.25)=27.25
(x-3.5)^2=27.25
(x-3.5)^2=27.25
We will continue.
x+-3.5=(+-)5.22015325
x=3.5(+-)5.22015325
Positive useful answer:
x=3.5+5.22015325
One worker is x=8.72015325
x+3=3+8.72015325
x+3=11.7201533
Other worker =11.7201533
check
1/x+1/(x+3)=1/5
1/8.72015325+1/(8.72015325+3)=1/5
1/8.72015325+1/11.7201533=1/5
11.7201533/102.201533+8.72015325/102.201533=1/5
20.4403065/102.201533=1/5
0.2=0.2
ok
Useless answer:
x=3.5-5.22015325
Useless answer is x=-1.72015325
x =-1.72015325
This answer is useless because it is Negative
For real life cases involving time, distance and other measurements, we reject the negative results
codewtp
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