Answer: (1) [tex]d = 25t+240\,,\,\,0\leq t\leq 6[/tex]; (2) 340 miles. See details below.
Explanation:
The key here is to know that given the speed and time traveled you can determine the (distance traveled) as (speed) x (time).
They want us to keep the time traveled for the first part of the journey as a variable, so let us do that. The speed during the first part is 65mph, so the distance for the first part is
[tex]d_1 = 65 \cdot t[/tex]
Knowin that the total ride was 6 hours, the distance in the second part (with speed of 40 mph) is as follows:
[tex]d_2 = 40 \cdot (6-t)[/tex]
So the total distance in terms of t is:
[tex]d = d_1 +d_2 = 65\cdot t + 40\cdot (6-t)=65t-40t+240\\d = 25t+240\,,\,\,0\leq t\leq 6[/tex]
(this is the answer to the first question). Note that t can range form 0 to 6 hours but outside of this range the expression is not applicable.
If we know t=4 hours:
[tex]d = 25\cdot4+240=340[/tex]
The answer to the second question is 340 miles.
