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Question 908450: Two people can solve a problem in 20 minutes. One of them
alone can solve that problem in 9 minutes less than the time
needed by the second person, how long would it take the
faster person working alone to solve the problem?
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! 1/x+1/(x+9)=1/20
(20*x*(x+9))/x+(20*x*(x+9))/(x+9)=(20*x*(x+9))/20
(20*(x+9))+20*x=x*(x+9)
20*x+180+20*x=x^2+9*x
40*x+180=x^2+9*x
x^2-31*x-180=0
Can it be factored?
What factors of -180 add up to -31?
Nevertheless, we will complete the square
x^2-31*x=180
add it
x^2-31*x+(-31/2)=180+(-31/2)
square it
x^2-31*x+(961/4)=180+(961/4)
x^2-31*x+(240.25)=180+(240.25)
x^2-31*x+(240.25)=420.25
(x-15.5)^2=420.25
(x-15.5)^2=420.25
we can continue
x-15.5=+-20.5
x=15.5+-20.5
Positive useful answer:
x=15.5+20.5
One answer is x=36
x+9=9+36
x+9=45
check
1/x+1/(x+9)=1/20
1/36+1/(36+9)=1/20
1/36+1/45=1/20
45/1620+36/1620=1/x
0.05=0.05
ok
Negative useless answer:
x=15.5-20.5
Negative answer is x=-5.0
For real life cases involving time, distance and other measurements, we reject the negative results
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