SOLUTION: Pls help me solve this word problem: Two men paint a home. Jim can paint it alone in 5 days and Alan in 8 days. They start to paint it together but after 2 days Alan gets sick and

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Question 407746: Pls help me solve this word problem:
Two men paint a home. Jim can paint it alone in 5 days and Alan in 8 days. They start to paint it together but after 2 days Alan gets sick and Jim finishes alone. How long does it take him to paint alone?
Thank you
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Two men paint a home. Jim can paint it alone in 5 days and Alan in 8 days. They start to paint it together but after 2 days Alan gets sick and Jim finishes alone. How long does it take him to paint alone?
Thank you
..
let x=days Jim works alone after Alan gets sick
Then 2+x =total days Jim works
Jim's daily work rate finishing the job alone=1/5
Alans's daily work rate finishing the job alone=1/8
Alan worked for 2 days, so he did 2(1/8) or 1/4 of the job
Jim worked for (2+x)days, so he did (2+x)(1/5)of the job to finish it.
2(1/8)+(2+x)(1/5)=100% of the job=1
1/4+(2+x)/5=1
5+8+4x=20
4x=7
x=7/4 days
ans:
Jim took 1+3/4 days working alone to finish the job.