Question 1198722
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There are many ways to solve a problem like this.  My preferred method is to take the given information and change one piece of data at a time to see how the required number of hours changes.<br>
Given: 5 men, 4 rooms takes 6 hours<br>
The new number of rooms is 28, which is 7 times as many.  7 times as many rooms and the same number of men means 7 times as many hours: 5 men, 4*7=28 rooms takes 6*7=42 hours<br>
The new number of men is 5+9=14; it increases by a factor of 14/5.  More men and the same number of rooms means fewer hours: 28 rooms, (14/5)*5 = 14 men means 42*(5/14) = 5*3 = 15 hours<br>
ANSWER: 15 hours<br>
Without all the words of explanation, the required number of hours is<br>
(6)*(28/4)*(5/14) = 15<br>
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And here is another of the many ways to solve the problem.<br>
4 rooms takes 5 men 6 hours, which means 30 man-hours for 4 rooms.
So 7 times as many rooms means 7 times as many man-hours: 210 man-hours for 28 rooms.
210 man-hours with 5+9=14 men means 210/14 = 15 hours.<br>
Again of course the answer is 15 hours.<br>