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?

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) (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

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
RELATED QUESTIONS
Together kim and chris sort recyclables in 2 hours and 55 minutes. Alone it takes kim 2... (answered by lwsshak3)

together it takes dawn and deb 2 hr 55 min to sort recyclables. alone dawn would require... (answered by ankor@dixie-net.com,MathTherapy)

Together, it takes John and Deb 2 hrs 55 min to sort recyclables. Alone, Jone would... (answered by Alan3354)

Working together, Kim and Chris can paint a room in 3 hours. Working alone, Chris can do... (answered by ikleyn)

I typed the question incorrect the first time, SORRY... Together,it takes John and Deb (answered by ankor@dixie-net.com)

together it takes ann and cindy 2 hr and 24 min to sort recyclable materials. alone ann... (answered by lwsshak3)

It takes Chris 1 1/2 times as long to clean the kitchen as Allison. It takes Allison 1... (answered by stanbon)

can some help me figure this out? Together John, Tina and Chris together completes the (answered by scott8148)

help me please? Together John, Tina and Chris together completes the yard in 1 hour and... (answered by scott8148)