Compare Proportional Relationships Quick Check
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Question
Use the image and table to answer the question.
A line graph is titled as Runner A, Average Minutes per Mile. The x-axis is labeled Minutes ranging from 0 to 36 in increments of 6. The y-axis is labeled Miles ranging from 0 to 4 in increments of 1. A solid line joins four plotted points. The coordinates of the plotted points are as follows: left parenthesis 0 comma 0 right parenthesis, left parenthesis 12 comma 1 right parenthesis, left parenthesis 24 comma 2 right parenthesis, and left parenthesis 36 comma 3 right parenthesis.
Runner B – Average Minutes per Miles
Minutes Miles
20 2
30 3
40 4
Runner A and Runner B tracked their mileage. Runner A’s average minutes per mile are displayed in the graph, and Runner B’s average minutes per mile are displayed in the table. Which runner has the fastest time, and what are their average minutes per mile?
(1 point)
Responses
To determine which runner has the fastest average time per mile, we need to calculate the average minutes per mile for each runner based on the data given.
For Runner A, we can use the points from the line graph:
- At 12 minutes, Runner A has run 1 mile.
- At 24 minutes, Runner A has run 2 miles.
- At 36 minutes, Runner A has run 3 miles.
From this, it's clear that Runner A's average is consistent: every 12 minutes, they run 1 mile, so Runner A's average minutes per mile is 12 minutes per mile.
Now let's analyze Runner B’s data from the table:
- At 20 minutes, Runner B has run 2 miles.
- At 30 minutes, Runner B has run 3 miles.
- At 40 minutes, Runner B has run 4 miles.
To find the average minutes per mile for Runner B, we can calculate the ratio for any of these entries. Let's use the first one:
20 minutes for 2 miles gives us 20 ÷ 2 = 10 minutes per mile.
Therefore, based on the average minutes per mile, Runner B is faster with an average of 10 minutes per mile compared to Runner A's average of 12 minutes per mile.