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So I was helping my brother with his homework question as follows

The voting office can handle $50 \space \text {voters/hour}$ and has 20 voting stations. How long does it take the average voter to vote?

He answered saying there are $60$ minutes for each machine, so $60 \space \text {minutes} \times 20 \space \text {machines} = 1200 \space \text {total voting minutes/ hour}$. Therefore there are $$= \frac {1200 \space \text {minutes}}{50 \text {votes}}$$ $$=24 \text {minutes/vote}$$

I can tell that the answer is wrong because $24$ minutes is too long for one person to vote. My answer is that since there $60$ minutes in an hour, and $50$ votes per hour then $$\frac {60}{50}$$ $$=1.2 \text {minutes}$$

I am not really sure why my brother's answer is incorrect; his method seems correct but is probably overcounting somehow. Any insight on the problem is appreciated

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    $\begingroup$ Maybe I missed something in the question, but as far as I can see your brother's answer is correct. I agree that 24 minutes is a long time for voting, but mathematics questions set for schoolwork are not always realistic. This is unfortunate because it gives students a very bad impression of the subject, but sadly, that's the way it (sometimes) is. $\endgroup$ – David Mar 2 '15 at 1:01
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    $\begingroup$ +1 for checking that the answer appears to be a realistic number, though. Pity that the problem fails to give realistic input data ... $\endgroup$ – hmakholm left over Monica Mar 2 '15 at 1:06
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    $\begingroup$ I would like to add that in some German state/city elections, a voter can distribute some 80 votes to named candidates (Panachage). It can take 24 minutes if the voters have not decided beforehand which candidates exactly they want. $\endgroup$ – Alexander Mar 2 '15 at 9:11
  • $\begingroup$ Hmm, I upvoted the question and explained why. So far 5 people have upvoted my comment with the explanation, but the question has only 3 upvotes in total. What's going on here, overcounting somehow? $\endgroup$ – hmakholm left over Monica Mar 2 '15 at 11:23
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Your brother's answer is actually absolutely correct. In your answer, you are calculating the average voting time if there was only one single voting machine, but there are $20$.

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Your answer ignores the fact that there are $20$ voting stations, presumably being used in parallel. If each voter took $1.2$ minutes and you kept a single station busy, you could handle $50$ per hour. Your brother is correct that averaged over a two hour period, you could afford each person to take $24$ minutes. Each station would handle $5$ people for a total of $100$, or $50$ per hour.

Probably your input data does not match reality. In my area we have only three voting stations and there are over 200 people in the precinct. Of course, not all show up, but they want to be able to handle a surge, not just the average level.

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  • $\begingroup$ +1 " you could afford each person to take 24 minutes": this is a much more intuitive interpretation, and I think more correct too $\endgroup$ – mattecapu Mar 2 '15 at 14:28

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