Jane and David are preparing for their annual trip to Yosemite. After careful analysis of route options, and based on traffic patterns, David determines the following:

Question

while driving at a constant pace, they will travel 40 miles in the first hour, 255 miles in the next 3 hours, and 120 miles in the next 2 hours.

I need an equation that will show David’s traveling time vs. distance when i graph it.

c. What does domain mean in the context of this situation? Identify the domain of the function.

d. What does range mean in the context of this situation? Identify the range of the function.

Answer 1

what you really need is to understand that speed = distance/time
they will travel 40 miles in the first hour, 255 miles in the next 3 hours, and 120 miles in the next 2 hours.
So, the speed changes for each trip segment. It is, in sequence,

40/1 = 40 mi/hr
255/3 = 85 mi/hr
120/2 = 60 mi/hr

Now, what do you need to provide?
traveling time vs. distance
That is, let x = the distance
and let y = the time
and recall that time = distance/speed.
So, now we know that y =
x/40 for 0 <= x < 40
1+(x-40)/85 for 40 <= x < 295
4+(x-295)/60 for 295 <= x <= 415

The rest should be doable now.