CPM Homework Help : PCT Problem 4-12

A car travels $45$ mph for $3$ hours and $55$ mph for the next two hours.

How far did the car travel?
Draw a speed vs. time graph of the situation.
What is the area under your curve from $0 ≤ h ≤ 5$ ?
How do your answers to part (a) and part (c) compare? Why?

Hint (a):

distance = (rate)(time)

Solution (a):

$(45)(3) + (55)(2)$

Answer (b): First quadrant graph, x axis labeled, time in hours, y axis labeled, speed in mph, horizontal segment from (0, comma 45), to (3, comma 45), then vertical to (3, comma 55), then horizontal to (5, comma 55).

Hint (c):

Added to graph, vertical segments from x axis to horizontal segments at x = 3, and x = 5, areas below horizontal segments are shaded.

Answer (d):

They are the same because the area under the curve is the distance traveled.