# How far from the home did Karen and her mother travel during the first hour of the trip? Calculate the average speed of the car during the first hour of the trip. How far did Karen and her mother travel during the second hour of the trip? Calculate the average speed of the car during the first two hours of the trip. Identify the time period(s) during the trip when the car was traveling at the greatest average speed. Identify the time period(s) during the trip when the car was stopped. Calculate the average speed of the car for the first three hours of the trip. If Karen and her mother take three hours to come home, calculate the average speed of the car for the trip home.

Calculate the average speed of the car during the first hour of the trip. The average speed during the first hour is the slope of the first green segment. That's . . . (change in 'y')/(change in 'x') = 40 miles/hour . How far did Karen and her mother travel during the second hour of the trip? -- Their distance at the end of the second hour is the same as it was at the beginning of that hour. They didn't budge during the second hour, and their average speed during that hour was zero. -- The line during the second hour is flat horizontal. Its slope is zero. On a distance/time graph, the slope of the line is speed. Calculate the average speed of the car during the first two hours of the trip. Average speed = (distance covered) / (time to cover the distance) = (40 miles) / (2 hours) = 20 miles/hour . Identify the time period(s) during the trip when the car was traveling at the greatest average speed. On a distance/time graph, the speed is the slope of the line. The greatest average speed is represented by the part of the graph where the slope is greatest. That looks like the entire first hour. Identify the time period(s) during the trip when the car was stopped. When the car was stopped, its speed was zero. On a distance/time graph, the slope of the line is speed. To find times when the car's speed was zero, we need to find parts of the line that are horizontal ... zero slope. That's the situation during the whole second hour and the whole fifth hour. Calculate the average speed of the car for the first three hours of the trip. Average speed = (distance covered) / (time to cover the distance) = (60 miles) / (3 hours) = 20 miles/hour . If Karen and her mother take three hours to come home, calculate the average speed of the car for the trip home. At the end of the graph, they are 75 miles from home. Their average speed on the return trip will be . . . (distance covered) / (time to cover the distance) = (75 miles) / (3 hours) = 25 miles/hour .