Question 890117
when he works alone, Brent takes 2 hours longer to buff the gymnasium floor than Tracy take when she works alone. After working for 3 hours, Brent quits and Tracy takes over. If it takes Tracy 2 hours to finish the rest of the floor how long would it have taken Brent to buff the entire floor? 
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let x=hrs tracy can do the job alone
1/x=her work rate
x+2=hrs Brent can do the job alone
1/(x+2)=his work rate
..
{{{(1/x+1/(x+2))*3+2/x=1}}}
lcd: x(x+2)
(x+2)*3+3x+2(x+2)=x^2+2x
3x+6+3x+2x+4=x^2+2x
x^2-6x-10
solve for x by quadratic formula:
x=7.3589
x+2=9.3589
how long would it have taken Brent to buff the entire floor? 9.36 hrs