Final answer:
The equation modeling the relationship between time (t) and distance (d) for a train traveling at a constant speed of 76.2 miles per hour is d = 76.2 * t.
Step-by-step explanation:
The question is asking to provide an equation that models the relationship between time (t) and distance (d) for a train traveling at a steady rate. The formula for this relationship is a linear equation since the train is traveling at a constant speed. The equation is derived from the formula for average speed, which is the total distance divided by the total time of travel.
In this case, the train's speed is 76.2 miles per hour, which can be used as the rate (v) in the equation. The general equation for distance as a function of time in a situation with constant speed is:
d = vt
Where:
- d = distance traveled
- v = steady rate of speed
- t = time
For this particular problem:
d = 76.2 * t
This equation means that to find the distance (d) the train has traveled, we multiply the time (t, in hours) by the speed (76.2 miles per hour).