Question 1199624
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You have received two responses showing very different ways to solve the problem using formal algebraic methods.<br>
Here is a quick and easy informal method for solving the problem.<br>
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.<br>
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.<br>
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.<br>
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:<br>
(8)*(4/7)*(7/4) = 8<br>
ANSWER: 8 hours<br>