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Paula can paint a room in six hours. Paula starts painting the room at
9:00 AM. At 11:00 AM, Carlos accompanies Paula, and both of them,
working together, finish painting the room at 2:30 PM. Assuming both
painters always paint at a constant rate, how many hours can Carlos
paint the same room working by himself?

 Oct 31, 2020
 #1
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Note that without Carlos 'helping' Paula would finish the room painting at 3 PM by herself....so Carlos is not a lot of help

   after painting ofr 2 hours  there is  4 hours left for Paula   to finish the job

      but it takes 3.5 hours with both of them

       1/4    + 1/ C = 1/ 3.5

           solve for C = 28    but this is for 2/3 of the job

                Carlos alone would be     28 * 3/2 = 42 hours to paint the room....he must have a very small brush?

 Oct 31, 2020
 #2
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Here is another way:

 

Since Carlos, working for 3.5 hours, saved her only 1/2 an hour, that means she does as much work in 1/2 an hour as Carlos does in 3.5 hours. Or Carlos rate is: 3.5 / 0.5 =7 times slower than that of Paula. And since she can paint the whole room in 6 hours, it would, therefore, take Carlos: 6  x  7 = 42 hours to finish the same room!!!!.

 Oct 31, 2020

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