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Both Andrew and Karleigh recorded the distance they ran in x minutes on treadmills.

Andrew
A 2-column table with 2 rows. Column 1 is labeled Time in Minutes with entries 18, 24. Column 2 is labeled Distance in miles with entries 1.5, 2.
Karleigh
A 2-column table with 2 rows. Column 1 is labeled Time in Minutes with entries 30, 40. Column 2 is labeled Distance in miles with entries 3, 4.

Andrew and Karleigh each run for 1 hour. Which statement explains who ran a greater distance?
Andrew ran a greater distance. The slope of the line described by the data in his table increased at a rate of StartFraction 1 Over 10 EndFraction mile per minute compared to Karleigh’s StartFraction 1 Over 12 EndFraction mile per minute.
Karleigh ran a greater distance. The slope of the line described by the data in her table increased at a rate of StartFraction 1 Over 10 EndFraction mile per minute compared to Andrew’s StartFraction 1 Over 12 EndFraction mile per minute.
Karleigh ran a greater distance. The slope of the line described by the data in her table increased at a rate of StartFraction 1 Over 12 EndFraction mile per minute compared to Andrew’s StartFraction 1 Over 10 EndFraction mile per minute.
Andrew ran a greater distance. The slope of the line described by the data in his table increased at a rate of StartFraction 1 Over 12 EndFraction mile per minute compared to Karleigh’s StartFraction 1 Over 10 EndFraction mile per minute.

1 answer

To determine who ran a greater distance, we can calculate the slopes for both Andrew and Karleigh based on their recorded distances over time.

Andrew's Data:

  • Time: 18 minutes, Distance: 1.5 miles
  • Time: 24 minutes, Distance: 2 miles

Calculating Andrew's slope: Change in Distance / Change in Time = (2 - 1.5) miles / (24 - 18) minutes = 0.5 miles / 6 minutes = 1/12 miles per minute.

Karleigh's Data:

  • Time: 30 minutes, Distance: 3 miles
  • Time: 40 minutes, Distance: 4 miles

Calculating Karleigh's slope: Change in Distance / Change in Time = (4 - 3) miles / (40 - 30) minutes = 1 mile / 10 minutes = 1/10 miles per minute.

Now we can summarize:

  • Andrew's slope is 1/12 miles per minute.
  • Karleigh's slope is 1/10 miles per minute.

Next, we will calculate the total distances that both Andrew and Karleigh would run in one hour (60 minutes):

For Andrew: At a rate of 1/12 miles per minute for 60 minutes: Distance = (1/12) * 60 = 5 miles.

For Karleigh: At a rate of 1/10 miles per minute for 60 minutes: Distance = (1/10) * 60 = 6 miles.

Conclusion: Karleigh ran a greater distance. The slope of the line described by the data in her table increased at a rate of 1/10 mile per minute compared to Andrew’s 1/12 mile per minute.

So the correct statement is: Karleigh ran a greater distance. The slope of the line described by the data in her table increased at a rate of StartFraction 1 Over 10 EndFraction mile per minute compared to Andrew’s StartFraction 1 Over 12 EndFraction mile per minute.