Question

Find the constant of proportionality and unit rate for the data in the table. Then write the equation to represent the relationship between time t and distance d
Time Distance
2 hrs 90 miles
3 hrs 135 miles
5 hrs 225 miles
6 hrs 270 miles
I need step by step... Please.

Answer 1

Time          Distance                Distance / Time

2hrs          90 miles                  90 miles / 2 hrs =  45 miles / hr

3hrs          135 miles                135 miles / 3 hrs =  45 miles / hr

5hrs          225 miles                 225 miles / 5 hrs =  45 miles / hr

6hrs          270 miles                  270 miles / 6 hrs =  45 miles / hr


Constant of proportionality is 45 miles / hr. This is the same for the four values. The unit rate is also 45 miles / hr.


Let us assume the Distance , d is directly proportional to Time, t

d α t

d = kt

Constant of proportionality is k which is D/T

d = 45t