Ashton, Alexa, and Clara want to know who types the fastest. The equation y = 39x models the rate at which Ashton can type. The table shows the relationship between words typed and... Ashton, Alexa, and Clara want to know who types the fastest. The equation y = 39x models the rate at which Ashton can type. The table shows the relationship between words typed and minutes for Alexa. The graph shows the same relationship for Clara. Who types the fastest? Read more

Steps to Solve

1. Understand Ashton's Typing Rate
   The typing rate for Ashton is modeled by the equation $y = 39x$, where $y$ is the number of words typed and $x$ is the time in minutes. This indicates that Ashton types 39 words per minute.

2. Calculate Words Typed by Ashton
   To find the number of words typed by Ashton in any given time, we substitute the values of $x$ from the equation. For example:

   • At $x = 2$: $y = 39(2) = 78$ words
   • At $x = 3$: $y = 39(3) = 117$ words
   • At $x = 4$: $y = 39(4) = 156$ words
   • At $x = 5$: $y = 39(5) = 195$ words

3. Analyze Alexa's Typing Rates from Table
   Extract the typing rates for Alexa from the provided table:

   • At 2 minutes: 78 words
   • At 3 minutes: 117 words
   • At 4 minutes: 156 words
   • At 5 minutes: 195 words

4. Look at Clara's Typing Rate from the Graph
   From the graph provided for Clara:

   • At 2 minutes: 78 words
   • At 4 minutes: 156 words
   • At 5 minutes: 195 words
   • At 8 minutes: 312 words

5. Calculate Typing Speeds
   Now calculate the typing speed for Clara by finding her words per minute based on the graph data:

   • At 8 minutes: Clara types 312 words, so her rate is $\frac{312 \text{ words}}{8 \text{ mins}} = 39 \text{ words/min}$.

6. Compare Typing Speeds
   Since both Ashton and Clara type at 39 words per minute, we need to review if there’s any unique timing in which someone types faster.
   Alexa's typing speed from the table has the same values at those minutes, confirming she also types 39 words per minute in the same time increments as per Ashton.