SOLUTION: Carolyn and Brian work in an accounting office. If they work together they can complete a corporate tax return in 2.5 hours. Working alone, it would take Brian 35 minutes longer

Question 656097: Carolyn and Brian work in an accounting office. If they work together they can complete a corporate tax return in 2.5 hours. Working alone, it would take Brian 35 minutes longer than Carolyn to complete the return. How long does it take each person working alone to finish the job?
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Carolyn and Brian work in an accounting office. If they work together they can complete a corporate tax return in 2.5 hours. Working alone, it would take Brian 35 minutes longer than Carolyn to complete the return. How long does it take each person working alone to finish the job?
**
use minutes for time
let x=time it takes Carolyn to finish the job working alone
1/x=her work rate
x+35=time it takes Brian to finish the job working alone
1/(x+35)=his work rate
2.5 hrs=150 min=given time it takes to finish the job working together
1/150=work rate working together
...
sum of individual work rates=work rate working together
(1/x)+1/(x+35)=1/150
LCD:x(x+35)
x+35+x=x(x+35)/150
2x+35=(x^2+35x)/150
300x+5250=x^2+35x
x^2-265x-5250=0
solve for x using following quadratic formula:

a=1, b=-265, c=-5250
ans: x≈283.5 min
x+35≈318.5 min
time it takes Carolyn to finish the job working alone≈283.5 min≈4.7 hrs
time it takes Brian to finish the job working alone=318.5 min≈5.3 hrs

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