Question

Time (hours) Distance (miles)
2 90
3 135
5 225
6 270

a. Find the constant of proportionality.

b. Use the constant of proportionality to write a unit rate for the data in the table.

c. Write an equation to represent the relationship between time, t, and distance, d.

Answer 1

a. To find the constant of proportionality, we need to divide the distance by the time for each set of data and then find the average:

Average rate = (90/2 + 135/3 + 225/5 + 270/6)/4
= 22.5 + 45 + 45 + 45
= 157.5

Therefore, the constant of proportionality is 157.5.

b. The unit rate is simply the constant of proportionality, which is 157.5 miles per hour.

c. We can write the equation as:

d = 157.5t

where d is the distance in miles and t is the time in hours.