<PRE><B>Question 736380</B>
&lt;b&gt;What we know:&lt;/b&gt;
beginning of day: &lt;i&gt;house is 1/5th painted&lt;/i&gt;
end of day: &lt;i&gt;house is 2/3rd painted&lt;/i&gt;
from beginning to end of day: &lt;i&gt;7 hours has passed&lt;/i&gt;

&lt;b&gt;What we want to know:&lt;/b&gt;
 (A) At what rate does the painter work? 
 (B) And, what units do we use to measure this?

&lt;b&gt;SOLUTION:&lt;/b&gt;

(1) Find the difference of the portion of the house that is painted at the beginning of the day and the portion of the house painted at the end of the day.

Let b = beg. = 1/5
      e = end = 2/3
      x = portion of house painted between beg. and end of day

Now,
      {{{x = e - b = 2/3 - 1/5 = 10/15 - 3/15 = 7/15}}}

So, the painter painted 7/15 of the house in 7 hours.

(2) Now express this as a rate:

Since the painter painted 7/15 of the house in 7 hours it is easy to see he/she painted 1/15 every hour.

     {{{(7/15)/7 = (7/15)*(1/7) = 1/15}}}
&lt;b&gt;ANSWER&lt;/b&gt;
Finally we can say that the rate of painting is (A) 1/15 house per hour, (B) where &lt;b&gt;house&lt;/b&gt; and &lt;b&gt;hour&lt;/b&gt; are our units.
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