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Machine A Produces 11 nails in 14 seconds.

Machine B produces 7 nails in 9 seconds.

Which is faster?

I thought that $\frac{11}{14}$ is larger than $\frac{7}{9}$ and thus A is the answer. However, the answer says that $\frac{9}{7}$ is bigger than $\frac{14}{11}$ so B is the answer. How does this work?

Wrzlprmft
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User3910
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  • The fractions compared in the answer are the inverse of your fractions, so it correct that the other one is larger, but doing the fractions like that is calculating how many minutes it takes to produce one nail, which should be lower for a faster machine. – Henrik supports the community Jun 12 '18 at 14:28
  • If you attach the units the text is computing seconds per nail. It is then confused when it claims more seconds per nail means faster. – Ross Millikan Jun 12 '18 at 15:03
  • @Dale Please recall that if the OP is solved you can evaluate to accept an answer among the given, more details here https://meta.stackexchange.com/questions/5234/how-does-accepting-an-answer-work – user Aug 04 '18 at 21:00

4 Answers4

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Your answer is correct. In 126 seconds (= 14 $\times$ 9), machine A produces $11 \times 9 = 99$ nails while machine B produces $7 \times 14 = 98$ nails. Therefore machine A is faster.

Allure
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You are right indeed

$$\frac 7 9 < \frac {11}{14}\iff7\cdot 14 <11\cdot9 \iff98<99$$

user
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If you make their denominators equal, you obtain $11/14={99\over14×9}$ and $7/9={7×14\over14×9}$. Since $99>7×14=98$, we have that $11/14>7/9$.

Allawonder
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What is the meaning of "Which is faster"? The answer depends on specific value. A is faster than B, If you need enough many nails.

However I understood the question. Your text's answer is correct, too. This answer compares each speed in one second.

Takahiro Waki
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