document.write( "Question 1199624: Let's say you have 4 painters that have completed 12 rooms in 8 hours. Assuming they are working at the same efficiency, how many hours does it take 7 painters to paint 21 rooms?
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Algebra.Com's Answer #833578 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "You have received two responses showing very different ways to solve the problem using formal algebraic methods.

\n" ); document.write( "Here is a quick and easy informal method for solving the problem.

\n" ); document.write( "From the first scenario to the second, the number of painters increases by a factor of 7/4. Increasing the number of painters decreases the required time, so the 8 hours in the first scenario gets multiplied by 4/7 because of the increased number of workers.

\n" ); document.write( "From the first scenario to the second, the number of rooms to be painted increases by a factor of 21/12 = 7/4. Increasing the number of rooms increases the required time, so the 8 hours in the first scenario gets multiplied by 7/4 because of the increased number of rooms.

\n" ); document.write( "Combining the effects of the increased number of workers and the increased number of rooms, the 8 hours in the first scenario gets multiplied by (4/7)(7/4) = 1 -- so the time required for the second scenario is the same 8 hours.

\n" ); document.write( "That's a lot of words to explain a simple method for solving the problem. Without all the words, the complete path to the solution is this:

\n" ); document.write( "(8)*(4/7)*(7/4) = 8

\n" ); document.write( "ANSWER: 8 hours

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