1961 AHSME Problems/Problem 15
Contents
Problem
If men working hours a day for days produce articles, then the number of articles (not necessarily an integer) produced by men working hours a day for days is:
Solution 1
Let be the number of articles produced per hour per person. By using dimensional analysis, Solving this yields . Using dimensional analysis again, the number of articles produced by men working hours a day for days is The answer is .
Solution 2 (Simple logic)
The question is based on the assumption that each person, each hour, each day, will be produce a constant number of items (maybe fractional).
So it takes men hours to produce item in a day.
In a similar manner, 1 man, 1 hour, for a day, can produce items. So men, hours a day, for days produce items. Therefore, the answer is .
Dimensional analysis is definitely the most rigid, but if you know the ending units (e.g. you know that density is measured in or something like that, you can just treat is as simple proportions and equations.
~hastapasta
What's happening here? Why isn't the answer ?
Notice that if we change the problem to men produce items a day, men produces how many items a day, then the answer would be . In this case, it would be a direct variation. However, notice that direct variations only have two factors --- an independent and dependent variable each (cause-effect, -). However, there are 3 factors, not 1, that are contributing to how many items are produced in the original problem. This is a combined variation problem, not a direct variation problem. This is the reason why the answer is (also see that the base unit (1 man/1 hour/1 day) is ).
Hope that solves your confusions.
~hastapasta
See Also
1961 AHSC (Problems • Answer Key • Resources) | ||
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Followed by Problem 16 | |
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