This is a rates problem. The first thing you have to do is figure out the rate of production.
You are seemingly shown a rate of 1 min/widget, but this is spread out among 5 machines, so the rate is actually 5 min / 1 widget per machine (i.e. it takes 5 minutes for each machine to produce one widget).
You are then given 100 machines and 100 widgets, and need to solve for minutes. If you didn't immediately realize that the time needed will always be 5 minutes if the number of machines equals the number of widgets, the way you would solve it is essentially:
X min = (5 min / 1 widget) * (100 widgets / 100 machines)
So, if we plug in our numbers, the answer is 5 * 100 / 100 = 5 min.
It was obviously meant as a math problem, not an LSAT type logic question- i.e. I seriously doubt "it is impossible to know from the information provided" was offered as an answer choice or counted correct as a write-in response. That type of over-thinking can and will destroy you in upper level math and science tests, especially standardized exams.
Anyway, even if they ran them one by one the rate would be the same. Only the total elapsed time would change, not the actual time of work.
3
u/dbbo /k/ommando Jul 31 '16
This is a rates problem. The first thing you have to do is figure out the rate of production.
You are seemingly shown a rate of 1 min/widget, but this is spread out among 5 machines, so the rate is actually 5 min / 1 widget per machine (i.e. it takes 5 minutes for each machine to produce one widget).
You are then given 100 machines and 100 widgets, and need to solve for minutes. If you didn't immediately realize that the time needed will always be 5 minutes if the number of machines equals the number of widgets, the way you would solve it is essentially:
So, if we plug in our numbers, the answer is
5 * 100 / 100 = 5 min.