SOLUTION: Together it takes Sally and Tom 42 minutes to complete a job. Alone, Sally completes the job 13 minutes faster than Tom. How long will it take tom to complete the job alone? 12 U A

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Together it takes Sally and Tom 42 minutes to complete a job. Alone, Sally completes the job 13 minutes faster than Tom. How long will it take tom to complete the job alone? 12 U A      Log On


   

Question 916669: Together it takes Sally and Tom 42 minutes to complete a job. Alone, Sally completes the job 13 minutes faster than Tom. How long will it take tom to complete the job alone? 12 U Advanced Functions question!
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Together it takes Sally and Tom 42 minutes to complete a job. Alone, Sally completes the job 13 minutes faster than Tom. How long will it take tom to complete the job alone?
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let x=time Tom can do the job alone
1/x=Tom's work rate
x-13=time Sally can do the job alone
1/(x-13)=Sally's work rate
42=time Sally and Tom working together can finish the job
1/42=their work rate
..
indv. work rates =work rate working together
1%2Fx%2B1%2F%28x-13%29=1%2F42
lcd:x(x-13)
x-13+x=x(x-13)/42
2x-13=(x^2-13x/42
84x-546=x^2-13x
x^2-97x+546=0
(x-6)(x-91)=0
x=91
time Tom can do the job alone=91 min