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The relationship between Amanda’s distance from school and time since she left school is linear, as shown in the table below.

time (hours): 0 , 1, 3
distance (miles): 3, 4.25, 6.75
Based on the table, determine whether each statement is true or false.
Amanda's distance increases by 1.25 miles each hour.

1 answer

To determine whether Amanda's distance increases by 1.25 miles each hour, let's analyze the data provided:

  • At time 0 hours, Amanda is 3 miles away from school.
  • At time 1 hour, Amanda is 4.25 miles away from school.
  • At time 3 hours, Amanda is 6.75 miles away from school.

Now, let's calculate the increase in distance between each time interval:

  1. From 0 hours to 1 hour: \[ 4.25 - 3 = 1.25 \text{ miles} \]

  2. From 1 hour to 3 hours: \[ 6.75 - 4.25 = 2.5 \text{ miles} \]

Next, we calculate the average increase per hour for the full duration from 0 to 3 hours:

  • The total distance traveled from 0 to 3 hours: \[ 6.75 - 3 = 3.75 \text{ miles} \]
  • The total time taken: \[ 3 - 0 = 3 \text{ hours} \]
  • The average rate of distance increase: \[ \frac{3.75 \text{ miles}}{3 \text{ hours}} = 1.25 \text{ miles per hour} \]

Based on this information, we confirm that Amanda's distance does indeed increase by 1.25 miles each hour on average.

So, the statement "Amanda's distance increases by 1.25 miles each hour." is true.