SOLUTION: Larry and Margee can paint a room in 7 hours. If Margee worked alone it would take her 3 hours longer than if Larry worked alone. How long would it take each person if they worke

Question 602226: Larry and Margee can paint a room in 7 hours. If Margee worked alone it would take her 3 hours longer than if Larry worked alone. How long would it take each person if they worked alone?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Larry and Margee can paint a room in 7 hours.
If Margee worked alone it would take her 3 hours longer than if Larry worked alone.
How long would it take each person if they worked alone?
:
Let t = L's time to do the job alone
then
(t=3) = M's time to do it
:
Let completed job = 1 (a painted room)
:
+ = 1
:
Multiply by t(t+3) to clear the denominators, results
7(t+3) + 7t = t(t+3)
7t + 21 + 7t = t^2 + 3t
14t + 21 = t^2 + 3t
0 = t^2 + 3t - 14t - 21
A quadratic equation
t^2 - 11t - 21 = 0
use the quadratic formula to find t

In this equation: x=t; a=1; b=-11; c=-21

The positive solution

t =
t = 12.65 hrs, time L takes working alone
then
12.65+3 = 15.65 hrs, time M takes working alone

RELATED QUESTIONS
Larry can paint a room in 8 hours by himself. After he worked for 2 hours, Patrick joins... (answered by stanbon)

If Joe can paint a house in ten hours and Larry can paint the same house in six hours how (answered by Alan3354)

Working together, Larry, Moe and Curly can paint an elephant in 3 minutes. Working... (answered by mananth)

Larry, Curly and Mo assembled a puzzle together in 40 hours. If Curly worked twice as... (answered by josmiceli)

An experienced worker can paint a room three times faster than her apprentice can.... (answered by jorel1380)

John can paint a room in 10 hours by himself. If kelly helps, they can paint the same... (answered by TimothyLamb)

It takes Larry 8 hours to paint his house. Larry started to paint the first 3 hours.... (answered by Theo,richwmiller)

Jamie,Pria and Paul can paint a room together in 2 hours if Pria does the job alone she... (answered by ikleyn)

Working together three men can paint a barn in six hours. If each man worked alone, the... (answered by lwsshak3)