SOLUTION: 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

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: 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      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

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?

Found 2 solutions by josgarithmetic, lwsshak3:
Answer by josgarithmetic(39626) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = time for Tracy to buff the floor.
Their work rates are:
Brent, 1%2F%28x%2B2%29
Tracy, 1%2Fx

The language used means that each of them works on the job separately not at the same time.

%281%2F%28x%2B2%29%293%2B%281%2Fx%29%2A2=1, their work accounts for one whole job of buffing the floor.
3%2F%28x%2B2%29%2B2%2Fx=1
3x%2B2%28x%2B2%29=x%28x%2B2%29 after multiplying both sides by the common denominator x(x+2).
3x%2B2x%2B4=x%5E2%2B2x
3x%2B4=x%5E2
x%5E2-3x-4=0
%28x%2B1%29%28x-4%29=0
The solution which has meaning is highlight%28x=4%29, the time for Tracy to do one whole job done alone.

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
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?
***
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
..
%281%2Fx%2B1%2F%28x%2B2%29%29%2A3%2B2%2Fx=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