SOLUTION: While assembling the sports car, the supervisor observed that it took ten men to assemble 2 sports cars in 3 days. The supervisor added 5 more men to do the job. How many days did
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Question 1151307: While assembling the sports car, the supervisor observed that it took ten men to assemble 2 sports cars in 3 days. The supervisor added 5 more men to do the job. How many days did it take them to assemble 9 sports cars?
Please solve thanks! Found 3 solutions by ikleyn, greenestamps, josgarithmetic:Answer by ikleyn(52775) (Show Source):
In the first case, there are 10 workers.
The rate of work is cars per day per worker.
In the second case, you have 10+5 = 15 workers.
The rate of work is cars per day per worker,
where d is the number of days to complete this job.
The number of "d" is unknown now and should be determined from the solution.
The rate of work is assumed to be the same in both cases.
It gives you this equation (a proportion)
= .
From this proportion, the product of the extreme terms is equal to the product of interior terms
2*d*15 = 10*3*9, or
2*d*15 = 2*5*3*9.
Canceling the common factors 2, 5 and 3 in both sides, you get
d = 9 days. ANSWER
Solved.
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The solution method shown by tutor @ikleyn is one of many common methods for solving problems like this.
For me, the quickest way to the answer to this problem is as follows:
(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.
(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.
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:
ANSWER: It take 9 days for the 15 men to assemble 9 sports cars.
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.
(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.
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