SOLUTION: Emily and Max can complete their math review in 6 hours working together. If Max works alone, he requires 5 hours more than Emily. How long does it take Emily to do the review wor

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Question 328669: Emily and Max can complete their math review in 6 hours working together. If Max
works alone, he requires 5 hours more than Emily. How long does it take Emily to do the review working alone?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
emily require x hours
Max requires x+5
..
emily can do the 1/x of the job in 1 hour
max can do 1/(x+5) of the job in 1 hour
..
Together they will do in 1%2Fx+%2B+1%2F%28x%2B5%29 hours
LCM = x(x+5)
+%28%28x%2B5%29%2Bx%29%2F%28x%2A%28x%2B5%29%29
%282x%2B5%29%2F%28x%2A%28x%2B5%29%29=6
%282x%2B5%29=%286%2Ax%2A%28x%2B5%29%29
2x%2B5=6x%5E2%2B30x
6x%5E2-2x%2B30x-5
6x%5E2%2B28x-5
find the roots of the equation x1,x2 using quadratic equation
x1=%28-b%2Bsqrt%28b%5E2-4%2Aa%2Ac%29%29%2F%282%2Aa%29
x1=%28-28%2Bsqrt%2828%5E2%2B120%29%29%2F12
x2=%28-28-sqrt%2828%5E2%2B120%29%29%2F12
x1= 0.17 hours --- Emily does it in 0.17 hours
x2= -4.8 hours ignore this value