Question 275821
I had a question about a work word problem. It says: Jane, Paul, and Peter can finish a painting in 2 hours. Jane can paint the same painting in 5 hours. Paul can paint it alone in 6 hours. How long would it take Peter to paint it on his own?

the equation was 1/5+1/6+1/x=1/2
and I dont understand where they got the 1/2 from.......If you could help me with this it would be great. Thanks!!!
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The key idea to solving these painting, mowing, job problems is to 
convert from time data to rate data.
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This is the idea:
If John takes 2 hrs/job his rate is 1/2 job/hr.
Notice that inverting the (hrs/job) you get (job/hr)
This converts time to do a job to the rate at which the job is done.
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So your 1/5 is a rate; your 1/6 is a rate; your 1/x is a rate
When you add those rates you get a rate; and 1/2 is a rate.
It is the rate associated with "finish the job in 2 hours".
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Cheers,
Stan H.