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 Miles per Minute. 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 Miles per Minute
Minutes Miles
20 2
30 3
40 4
Runner A and Runner B tracked their mileage. Runner A’s average miles per minute are displayed in the graph, and Runner B’s average miles per minute are displayed in the table. Which runner has the fastest time, and what are their average miles per minute?
(1 point)
Responses
Runner A has the fastest time at 12 average miles per minute.
Runner A has the fastest time at 12 average miles per minute.
Runner A has the fastest time at 10 average miles per minute.
Runner A has the fastest time at 10 average miles per minute.
Runner B has the fastest time at 12 average miles per minute.
Runner B has the fastest time at 12 average miles per minute.
Runner B has the fastest time at 10 average miles per minute.
Runner B has the fastest time at 10 average miles per minute.
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Runner A has the fastest time at 12 average miles per minute.
To determine which runner has the fastest time and what their average miles per minute are, we can compare the values in the table to the coordinates of the plotted points on the graph.
From the table, we can see that Runner B's average miles per minute are:
- 20 minutes: 2 miles
- 30 minutes: 3 miles
- 40 minutes: 4 miles
From the graph, Runner A's average miles per minute can be determined from the plotted points:
- At 12 minutes: 1 mile
- At 24 minutes: 2 miles
- At 36 minutes: 3 miles
Comparing these values, we can see that both Runner A and Runner B have an average of 1 mile at 12 minutes. However, at 24 and 36 minutes, Runner A has a faster time with 2 and 3 miles respectively, while Runner B only has 2 and 3 miles at 30 and 40 minutes.
Therefore, the correct answer is: Runner A has the fastest time at 12 average miles per minute.
To compare the average miles per minute for Runner A and Runner B, we need to look at the information given in the image and table.
First, let's analyze the graph for Runner A. The x-axis represents minutes and ranges from 0 to 36 in increments of 6, while the y-axis represents miles and ranges from 0 to 4 in increments of 1. A solid line joins four plotted points: (0,0), (12,1), (24,2), and (36,3). This means that at 0 minutes, Runner A covered 0 miles, at 12 minutes they covered 1 mile, at 24 minutes they covered 2 miles, and at 36 minutes they covered 3 miles.
Now, let's look at the table for Runner B. It shows the average miles per minute for Runner B at different time intervals. According to the table, at 20 minutes, Runner B covered 2 miles, at 30 minutes they covered 3 miles, and at 40 minutes they covered 4 miles.
To determine which runner has the fastest time, we need to compare their average miles per minute.
For Runner A, we can calculate the average miles per minute by dividing the total miles covered by the total time elapsed. From the graph, we see that Runner A covered 3 miles in 36 minutes. So, the average miles per minute for Runner A is 3 miles / 36 minutes = 1/12 miles per minute.
For Runner B, we can directly read the average miles per minute from the table. According to the table, Runner B covered 2 miles in 20 minutes, so the average miles per minute for Runner B is 2 miles / 20 minutes = 1/10 miles per minute.
Comparing the average miles per minute for Runner A and Runner B, we can see that Runner A has the fastest time at a rate of 1/12 miles per minute. Therefore, the correct answer is: Runner A has the fastest time at 12 average miles per minute.