6. At \( 1: 00 \mathrm{pm} \), you had typed 62 words of your ELA report. At \( 1: 15 \mathrm{pm} \), you had typed 392 words. During this time, how many words did you type per minute? Toll whether the ratios form a proportion. Explain your answer.

To determine how many words you typed per minute and whether the ratios form a proportion, let's break down the problem step by step. ### **1. Calculating Words Typed Per Minute** - **Initial Word Count at 1:00 pm:** 62 words - **Word Count at 1:15 pm:** 392 words - **Time Elapsed:** 15 minutes (from 1:00 pm to 1:15 pm) **Words Typed During This Period:** \[ 392 \text{ words} - 62 \text{ words} = 330 \text{ words} \] **Words Per Minute (WPM):** \[ \frac{330 \text{ words}}{15 \text{ minutes}} = 22 \text{ WPM} \] So, you typed **22 words per minute** during this 15-minute interval. ### **2. Assessing Whether the Ratios Form a Proportion** A **proportion** is an equation that states that two ratios are equal. In this context, we're examining whether the relationship between words typed and time is consistent, indicating a constant typing rate. Let's consider two points in time: - **At 1:00 pm:** 62 words - **At 1:15 pm:** 392 words To determine if these form a proportion, we can set up the ratios of words to time for two different instances and see if they are equal. However, since we only have two data points, we can infer that if the rate (words per minute) remains constant between these points, the ratios do form a proportion. **Verification:** 1. **From 1:00 pm to 1:15 pm:** \[ \text{WPM} = \frac{330 \text{ words}}{15 \text{ minutes}} = 22 \text{ WPM} \] 2. **Assuming Consistency:** - If you were to project this rate forward or backward, the relationship between words and time would remain proportional. Since the typing rate is consistent (22 WPM) over the given time interval, **the ratios do form a proportion**. This means that the number of words typed is directly proportional to the time spent typing, confirming a steady and constant typing speed. ### **Summary** - **Words Typed Per Minute:** 22 WPM - **Do the Ratios Form a Proportion?** Yes, because the number of words typed is directly proportional to the time spent typing, indicating a constant typing rate. **Answer:** You typed 22 words each minute. Additionally, the word counts and times are proportional since words are increasing at a constant rate, so the ratios do form a proportion.