Question

n airplane's distance traveled is monitored over time. The results are displayed in this table.

Time (h) 1 2 3 4
Distance traveled (mi) 560 1120 1680 2240
What is the constant of proportionality of this proportional relationship?

Answer 1

To find the constant of proportionality in this relationship, we can use the formula for the constant of proportionality, which is the ratio of distance traveled to time.

From the table:
- When \( t = 1 \) hour, distance = 560 miles
- When \( t = 2 \) hours, distance = 1120 miles
- When \( t = 3 \) hours, distance = 1680 miles
- When \( t = 4 \) hours, distance = 2240 miles

To calculate the constant of proportionality (\( k \)), we can compute the ratio of distance to time for any of the time intervals.

Using the first entry:
\[
k = \frac{\text{Distance}}{\text{Time}} = \frac{560 \text{ miles}}{1 \text{ hour}} = 560 \text{ mph}
\]

You can also check using another entry, for example the second entry:
\[
k = \frac{1120 \text{ miles}}{2 \text{ hours}} = 560 \text{ mph}
\]

For the third entry:
\[
k = \frac{1680 \text{ miles}}{3 \text{ hours}} = 560 \text{ mph}
\]

For the fourth entry:
\[
k = \frac{2240 \text{ miles}}{4 \text{ hours}} = 560 \text{ mph}
\]

Thus, the constant of proportionality in this relationship is \( **560 \text{ mph}** \).