# How long does it take the average voter to vote?

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

• 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. – David Mar 2 '15 at 1:01
• +1 for checking that the answer appears to be a realistic number, though. Pity that the problem fails to give realistic input data ... – hmakholm left over Monica Mar 2 '15 at 1:06
• 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. – Alexander Mar 2 '15 at 9:11
• 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? – hmakholm left over Monica Mar 2 '15 at 11:23

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 $20$.
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.