Ahorse ran 800 meters in 40 seconds , 1200 meters in 60 seconds , and 480 meters in 24 seconds . is this a proportional relationship? if so , what is the constant proportionally? what does it represent ? write an equation to represent the distant d , in meter , that the horse runs is seconds

This is a proportional relationship, the constant of proportionality is 20m/s and it represents that the horse can run 20 meters every second.  

Equation:  d = 20s, where d=distance and s=number of seconds.

Step-by-step explanation:

In order to find out whether this relationship is proportional, you need to see if the rate at which the horse runs is constant (the same).  If you look at the three sets of data (24, 480), (40, 800) and (60, 1200) where the pair is (seconds, meters), you can see that for any two sets of data the change in meters divided by the change in seconds is consistently 20m/s.  For example:

Since the constant is 20, we know that the horse can run 20 meters every second.  To find the horse's total distance, we need to multiply the rate by the number of seconds that it runs:

d = 20s