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
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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) (Show Source): You can put this solution on YOUR website!
Let x = time for Tracy to buff the floor.
Their work rates are:
Brent,
Tracy,
The language used means that each of them works on the job separately not at the same time.
, their work accounts for one whole job of buffing the floor.
after multiplying both sides by the common denominator x(x+2).
The solution which has meaning is , the time for Tracy to do one whole job done alone.
Answer by lwsshak3(11628) (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
..
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
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