SOLUTION: Carl can paint a room 3 hours faster than Jennifer can. If they work together, they can complete the job in 2 hours. Using complete sentences, explain each step in figuring out how

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Carl can paint a room 3 hours faster than Jennifer can. If they work together, they can complete the job in 2 hours. Using complete sentences, explain each step in figuring out how      Log On


   

Question 1025423: Carl can paint a room 3 hours faster than Jennifer can. If they work together, they can complete the job in 2 hours. Using complete sentences, explain each step in figuring out how to determine the time it would take Jennifer to complete this job on her own.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Painter            Rate as ROOM/HOURS
Carl                 1%2F%28x-3%29
Jennifer             1%2Fx
Both Combined        1%2F2


highlight_green%281%2F%28x-3%29%2B1%2Fx=1%2F2%29

2x%28x-3%29%281%2F%28x-3%29%2B1%2Fx%29=2x%28x-3%29%281%2F2%29

2x%2B2%28x-3%29=x%28x-3%29

2x%2B2x-6=x%5E2-3x

7x-6=x%5E2

x%5E2-7x%2B6=0
(Yes, this IS factorable... see below.)

x=%287%2B-+sqrt%2849-4%2A6%29%29%2F2
x=%287%2B-+sqrt%2849-24%29%29%2F2

x=%287%2B-+5%29%2F2

x=system%281%2COR%2C6%29---------but obviously one one of these can make any sense.

Jennifer paints the room herself in 6 hours.



---
x%5E2-7x%2B6
%28x-6%29%28x-1%29