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
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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
