Julieta has been in the car with her family on a road trip for the past three hours. For
the first hour, they went about 55 mph. Then, the speed limit changed and they
started going about 70 mph. They are still going 70 mph.
A. Create a graph that models the distance Julieta’s family has traveled over time
during their road trip.
B. What does the slope of your graph at any given time represent? Explain.
C. Create a piecewise function that models the distance Julieta's family has
traveled over time.
D. Two and a half hours into the road trip, how far had Julieta’s family traveled?
Give your answer to a reasonable level of accuracy. Explain why your response
cannot be perfectly accurate.
E. Write your own question that asks a student to interpret a different feature of
your graph/function in terms of the given context. Then, provide the solution
for your question.
A.
B. The slope of the graph represents the speed at which Julieta's family is traveling. In this case, since they are traveling at a constant speed of 70 mph, the slope of the graph is a straight line.
C. Let D(t) represent the distance traveled by Julieta's family after t hours.
D(t) =
- 55t if 0 ≤ t < 1
- 55 + 70(t-1) if 1 ≤ t
D. Two and a half hours into the road trip, Julieta's family had traveled 150 miles. This calculation is not perfectly accurate because it assumes that the speed of 55 mph is maintained for the first hour and then the speed of 70 mph is maintained for the rest of the trip without any variations.
E. How can you determine the average speed of Julieta's family during the first 2 hours of the road trip?
Solution: To calculate the average speed during the first 2 hours, divide the total distance traveled in the first 2 hours by 2.
Distance traveled in the first 2 hours = 55 mph * 2 hours = 110 miles
Therefore, the average speed during the first 2 hours is 55 mph.