SOLUTION: After 5 hours of painting, Jess asked the assistance of Jon. Together they finished the job in 4 more hours. Had Jon joined in an hour after Jess started working, the job would hav

Algebra ->  Rate-of-work-word-problems -> SOLUTION: After 5 hours of painting, Jess asked the assistance of Jon. Together they finished the job in 4 more hours. Had Jon joined in an hour after Jess started working, the job would hav      Log On


   

Question 631013: After 5 hours of painting, Jess asked the assistance of Jon. Together they finished the job in 4 more hours. Had Jon joined in an hour after Jess started working, the job would have been finished in 7 hours. How long would it have taken Jess to paint the house alone
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +r%5B1%5D+ = Jess's rate of painting in jobs/hr
Let +r%5B2%5D+ = Jon's rate of painting in jobs/hr
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In 5 hours Jess gets +5r%5B1%5D+ fraction of the job done
In 1 hour jess get +1%2Ar%5B1%5D+ fraction of the job done
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given:
(1) +5r%5B1%5D+%2B+4%2A%28+r%5B1%5D+%2B+r%5B2%5D+%29+=+1+ ( 1 means the whole job is done )
(2) +1%2Ar%5B1%5D+%2B+7%2A%28+r%5B1%5D+%2B+r%5B2%5D+%29+=+1+
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(1) +9r%5B1%5D+%2B+4r%5B2%5D+=+1+
(2) +8r%5B1%5D+%2B+7r%5B2%5D+=+1+
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Multiply both sides of (1) by +7+
Multiply both sides of (2) by +4+
and subtract (2) from (1)
(1) +63r%5B1%5D+%2B+28r%5B2%5D+=+7+
(2) +-32r%5B1%5D+-+28r%5B2%5D+=+-4+
+31r%5B1%5D+=+3+
+r%5B1%5D+=+3%2F31+
This means Jess can paint 3 houses in 31 hrs
+3%2F31+=+1%2Fx+
+10.333+
He could paint the house alone in 10 hrs and 20 min
check:
(1) +9%2A%283%2F31%29+%2B+4r%5B2%5D+=+1+
(1) +4r%5B2%5D+=+31%2F31+-+27%2F31+
(1) +4r%5B2%5D+=+4%2F31+
(1) +r%5B2%5D+=+1%2F31+
and
(2) +8%2A%283%2F31%29+%2B+7%2A%281%2F31%29+=+1+
(2) +24%2F31+%2B+7%2F31+=+31%2F31+
(2) +24+%2B+7+=+31+
(2) +31+=+31+
OK