SOLUTION: While building the addition to Ponderosa High School, the electricians found that it took 5 men to wire 4 rooms in 6 hours. The foreman added 9 more men to the job. How many hours

Question 1198722: While building the addition to Ponderosa High School, the electricians found that it took 5 men to wire 4 rooms in 6 hours. The foreman added 9 more men to the job. How many hours would it take them to do 28 rooms?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

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.

Given: 5 men, 4 rooms takes 6 hours

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

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

ANSWER: 15 hours

Without all the words of explanation, the required number of hours is

(6)*(28/4)*(5/14) = 15

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And here is another of the many ways to solve the problem.

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.

Again of course the answer is 15 hours.

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