SOLUTION: Together, it takes Kim and Chris 2hours and 55minutes to sort recyclables. Alone Kim would require 2 hours more than Chris. How long would it take Chris to do the job?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Together, it takes Kim and Chris 2hours and 55minutes to sort recyclables. Alone Kim would require 2 hours more than Chris. How long would it take Chris to do the job?       Log On


   

Question 469115: Together, it takes Kim and Chris 2hours and 55minutes to sort recyclables. Alone Kim would require 2 hours more than Chris. How long would it take Chris to do the job?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Kim takes x hours
Chris takes x+ 2 hours
Kim does 1/x of the job in 1 hour
Chris takes1/(x+ 2)of the job in 1 hour
Together they take 1/x+ 1/(x+2)of the job in 1hour
Together they do the job in 2 8/9 hours
Together they do 1/(2 8/9) of the job in 1 hour
1/x+1/(x+2)=1/(26/9)
LCD =x(x+2)
(x+2)+x= 1/(26/9)(x^2+2)x
( 2x+2)* 26/9 =(x^2+2x
5.83x+5.83 = x^2+ 2 x
x^2 -3.83 x -5.83 = 0
Find the roots of the equation by quadratic formula

a= 1 b= -3.83 c= -5.83

b^2-4ac= 14.67 + 23.32
b^2-4ac= 37.99
sqrt( 37.99 )= 6.16
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=( 3.83 + 6.16 )/ 2
x1= 5
x2=( 3.83 -6.16 ) / 2
x2= -1.17
Ignore negative value
Chris will take 5 hours