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Difference between revisions of "2023 SSMO Accuracy Round Problems/Problem 1"
 
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Then it takes him <cmath>23 \cdot 500 + (499 - 99) \cdot 0.5 + 99 \cdot 2 = 11898</cmath> seconds to read the entire passage.
 
Then it takes him <cmath>23 \cdot 500 + (499 - 99) \cdot 0.5 + 99 \cdot 2 = 11898</cmath> seconds to read the entire passage.
  
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Then, <math>10S</math> is <math>\frac{10}{60} = \frac16</math> of this  
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So, <math>10S</math> is <math>\frac{10}{60} = \frac16</math> of this value, so <math>\lfloor 10S \rfloor = \boxed{1983}.</math>
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value, so <math>\lfloor 10S \rfloor = \boxed{1983}.</math>
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~SMO_Team

Latest revision as of 14:44, 9 September 2025

Problem

Mr. Sammy proposes a Hamburger Proclamation, which has $500$ lines, divided into paragraphs of $5$ lines each. It takes him $23$ seconds to read each line. Additionally, he adds a $0.5$ second pause between two lines in a paragraph, and a $2$ second pause between paragraphs. If it takes him $S$ minutes to read the whole Hamburger Proclamation, find $\left\lfloor 10S \right\rfloor.$

Solution

There are $100$ paragraphs, so there are $499$ pauses between all lines and $99$ pauses between paragraphs.

Then it takes him \[23 \cdot 500 + (499 - 99) \cdot 0.5 + 99 \cdot 2 = 11898\] seconds to read the entire passage.

So, $10S$ is $\frac{10}{60} = \frac16$ of this value, so $\lfloor 10S \rfloor = \boxed{1983}.$

~SMO_Team

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