SOLUTION: A man can paint a room in 8 hours. It takes his son 12 hours to do the same job. After working by himself for 2 hours, his son joined him and together they finished the job. How lo

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A man can paint a room in 8 hours. It takes his son 12 hours to do the same job. After working by himself for 2 hours, his son joined him and together they finished the job. How lo      Log On


   

Question 1088529: A man can paint a room in 8 hours. It takes his son 12 hours to do the same job. After working by himself for 2 hours, his son joined him and together they finished the job. How long did the son work?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The man's rate of working is
[ 1 room painted ] / [ 8 hrs ] = +1%2F8+
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[ rate ] x [ time in hrs ] = [ fraction of the job completed ]
+%281%2F8%29%2A2+=+1%2F4+
That means there is +3%2F4+ of the job left to do
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Add their rates of working to get the rate at which
they will finish 3/4 of the job in +t+ hrs
+1%2F8+%2B+1%2F12+=+%28%283%2F4%29%29+%2F+t+
Multiply both sides by +24t+
+3t+%2B+2t+=+18+
+5t+=+18+
+t+=+3.6+
+.6%2A60+=+36+
The son worked for 3 hrs and 36 min
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Get a 2nd opinion if needed