You start 50 miles east of Pittsburgh and drive east at a constant speed of 65 miles per hour. (Assume that the road is straight and permits you to do this.) Find a formula for d, your distance from Pittsburgh, as a function of t, the number of hours of travel.
d = 50 + 65t
To find a formula for the distance from Pittsburgh as a function of time, we need to consider that the distance is changing at a constant speed of 65 miles per hour.
Let's consider the starting point as d = 0 when t = 0, which means the distance from Pittsburgh is 0 when you start the journey.
Since you are driving at a constant speed of 65 miles per hour, the formula for distance (d) can be written as:
d = speed × time
We know that the speed is 65 miles per hour, so we can substitute it into the formula:
d = 65t
Therefore, the formula for d, your distance from Pittsburgh, as a function of t, the number of hours of travel, is:
d(t) = 65t
This formula tells us that for each hour you travel, the distance from Pittsburgh will increase by 65 miles.