express distance as a function of time traveled.

jason leaves detroit @ 2pm & drives at constant speed west. he passes ann arbor, 40 mi. from detroit at 2:50 pm.

i understand that d=rt. but i'm stuck.
is this the answer-- d(t)=t/rt ??

You could make a table like this
2pm 0m Detroit
2:50 40m Ann Arbor
or you could determine an average rate as
40mi/50min = 4/5 mi/min * 60min/hr = 48mi/hr
I'm not entirely sure what the question is asking for either, so re-read to see if there's any clue somewhere.

To express distance as a function of time traveled, you need to determine the relationship between the distance and the time. In this scenario, Jason leaves Detroit at 2 pm and passes Ann Arbor, which is 40 miles away from Detroit, at 2:50 pm.

First, let's determine the time difference between 2 pm and 2:50 pm. It is 50 minutes.

Now, let's calculate the average speed at which Jason is driving. Divide the distance traveled (40 miles) by the time taken (50 minutes):

Average speed = 40 miles / 50 minutes.

To express this average speed in miles per hour, convert the time to hours:

Average speed = (40 miles / 50 minutes) * (60 minutes / 1 hour).

Simplifying, we get:

Average speed = (40 / 50) * (60 / 1) miles per hour.

Average speed = 48 miles per hour.

Now that we know the average speed, we can express the distance traveled as a function of time using the formula d = rt, where d is the distance, r is the rate or speed, and t is the time:

Distance traveled (d) = Rate (r) * Time elapsed (t).

Substituting the known values:

d = 48 miles per hour * t.

So, the function expressing the distance traveled as a function of time is:

d(t) = 48t.

Note that the units of time should be consistent with the units of speed. In this case, since the speed is in miles per hour, the time should be in hours.