Question 1151307
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The solution method shown by tutor @ikleyn is one of many common methods for solving problems like this.<br>
For me, the quickest way to the answer to this problem is as follows:<br>
(1) In going from 10 men on the job to 15 men on the job, the number of men gets multiplied by 15/10 = 3/2/  Since more men means less time to do the job, that means the time required to do the job gets multiplied by 2/3.<br>
(2) In changing the number of cars from 2 to 9, the amount of time required to do the job gets multiplied by 9/2.<br>
So the 3 days it takes the 10 men to assemble 2 sports cars gets multiplied by 2/3 because of the increased number of workers and by 9/2 because of the increased number of sports cars:<br>
{{{(3)(2/3)(9/2) = 9}}}<br>
ANSWER: It take 9 days for the 15 men to assemble 9 sports cars.<br>
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While that is my personal favorite for a solution method for the problem, here is another common method that is also different than the method shown by tutor @ikleyn.<br>
(1) It takes 10 men 3 days to assemble 2 sports cars.  That is 10*3 = 30 man-days to assemble 2 cars.
(2) That means it takes 30/2 = 15 man-days to assemble 1 car.
(3) That means it takes 15*9 = 135 man-days to assemble 9 cars.
(4) And that means the number of days it takes 15 men to assemble 9 cars is 135/15 = 9.<br>