Question 1122097: a. what is a graph that displays David’s traveling time vs. distance.
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:
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.
b. what is a piecewise function representing Jane and David’s traveling time and distance?
c. What is the domain and what does it mean in the context of this situation?
d. What is the range and what does it mean in the context of this situation?
e. What assumptions (if any) are being made in the context of this situation? Are they realistic?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! D=40+85(3)+60(2), since the pace is constant (presumably constant for each part, not the whole thing).
The domain is [0, 6] This is the duration of the 6 hour trip.
The range is [0. 415] This is the possible miles traveled during any time in the domain.
The assumptions are constant speed for the entire hour for the first, three hours for the middle, and 2 hours for the end. It is possible to do so, but it would be difficult.
Use inequalities for the following (mine weren't supported)
Between 0 and 1 hour, distance is 40t. (t measured in hours)
Between 1 and 4 hours, distance is 40+85(t-1)
From 4 to 6 hours, distance is 295+60(t-4)
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