SOLUTION: It takes Jake, 14h to repair a car’s transmission. After he had worked for 7 h, Alice began to help him. Together, they finished the job in 3 more hours. How long would it take Ali

Algebra ->  Rate-of-work-word-problems -> SOLUTION: It takes Jake, 14h to repair a car’s transmission. After he had worked for 7 h, Alice began to help him. Together, they finished the job in 3 more hours. How long would it take Ali      Log On


   

Question 560647: It takes Jake, 14h to repair a car’s transmission. After he had worked for 7 h, Alice began to help him. Together, they finished the job in 3 more hours. How long would it take Alice to do the job alone?
I attempted to do this problem like I did the other one's by assigning a variable to the unknown amout of time worked by Alice. Then I got stuck when I tried to find the rate for both. And I think I'm supposed to subtract somewhere. Any help would be appreciated.
Found 2 solutions by scott8148, itsmers123nj:
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
Jake had completed half of the job (7/14) when Alice began

they each do some fraction of half the job based on their individual rates ___ (3 / 14) + (3 / x) = 1/2

multiplying by 14x ___ 3x + 42 = 7x

Answer by itsmers123nj(1) About Me  (Show Source):
You can put this solution on YOUR website!
x = time Alice works alone.
14h = time Jake works alone.
Jake: 7+3 = 10(1/14) = 10/14 = 5/7
Alice: 1/x(3)=3/x
SOLUTION: 5/7+3/x=1 (LCM = 14x)
14n(5/7+3/x)=1(14n)->10x+42=14x-> x = 21/2 = 10.5
ANSWER: It would take Alice 10h 30m to repair the transmission if she works alone.