Question

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.

Answer 1

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**.