SOLUTION: 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
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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!!!
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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.
----
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.
==============================
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".
====================
Cheers,
Stan H.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
If person A can complete an entire job in 
time periods, then that person can complete 
of the job in one time period. Jane can do the whole job in 5 hours, so she can do 
of the job in one hour. Likewise, Paul is 6 hours and 
of the job, while Peter is hours and of the job. In the same way, the three of them working together can do the job in 2 hours, which is to say that the three of them working together can do 
of the job in one hour.
The equation works out to "The fraction of the job that Jane can do in one hour" plus "The fraction of the job that Paul can do in one hour" plus "The fraction of the job that Peter can do in one hour" adds up to "The fraction of the job that the three of them working together can do in one hour"
John
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