SOLUTION: word problem involving quadratic equation working together, kim and dominic can paint their apartment in 2 days.working alone,kim can complete the job in 3 days less than dominic,

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Question 669267: word problem involving quadratic equation
working together, kim and dominic can paint their apartment in 2 days.working alone,kim can complete the job in 3 days less than dominic, working alone.how long would it take each person working alone?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
kim and dominic can paint their apartment in 2 days.
working alone,kim can complete the job in 3 days less than dominic, working alone.
how long would it take each person working alone?
:
let t = time required by Kim to do the job
then
(t+3) = time required by Dom
:
Let the completed job = 1; (a painted room)
:
A typical shared work equation
2%2Ft + 2%2F%28%28t%2B3%29%29 = 1
Multiply by t(t+3), cancel the denominators:
2(t+3) + 2t = t(t+3)
2t + 6 + 2t = t^2 + 3t
Combine as a quadratic on the right
0 = t^2 + 3t - 4t - 6
t^2 - t - 6 = 0
factors to
(t-3)(t+2) = 0
the positive solution
t = 3 days, Kim working alone
then
3 + 3 = 6 days, Dome working alone
:
:
Check this
2/3 + 2/6 = 1