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Question 908183: Working together, Brian and Collin can solve a hard math problem in 15 minutes. On Monday, Collin worked alone and on Tuesday, Brian worked alone. If it took Brian 6 more minutes to solve the hard problems alone than Collin took, how long did it take Brian and Collin to solve them individually?
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! 1/x+1/(x+6)=1/15
(15*x*(x+6))/x+(15*x*(x+6))/(x+6)=(15*x*(x+6))/15
(15*(x+6))+15*x=x*(x+6)
15*x+90+15*x=x^2+6*x
30*x+90=x^2+6*x
x^2-24*x-90=0
Can it be factored?
What factors of -90 add up to -24?
Nevertheless, we will complete the square
x^2-24*x=90
add it
x^2-24*x+(-24/2)=90+(-24/2)
square it
x^2-24*x+(576/4)=90+(576/4)
x^2-24*x+(144)=90+(144)
x^2-24*x+(144)=234
(x-12)^2=234
(x-12)^2=234
we can continue
x-12=+-15.2970585
x=12+-15.2970585
Positive useful answer:
x=12+15.2970585
One answer is x=27.2970585
x+6=6+27.2970585
x+6=33.2970585
check
1/x+1/(x+6)=1/15
1/27.2970585+1/(27.2970585+6)=1/15
1/27.2970585+1/33.2970585=1/15
0.36633984e-1+0.30032683e-1=0.66666667e-1
0.66666667e-1=0.66666667e-1
ok
Negative useless answer:
x=12-15.2970585
Negative answer is x=-3.29705854
For real life cases involving time, distance and other measurements, we reject the negative results
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