Question 29·Medium·Ratios, Rates, Proportional Relationships, and Units
The graph shows the distance, in miles, that a hiker traveled as a function of time, in minutes.
The hiker took a break whenever the distance stayed the same.
Which choice is the hiker’s average speed while moving, in miles per hour?
For an average speed question, first identify the total distance from the beginning and end of the graph. Then determine how long the person is actually moving by excluding any flat (constant distance) sections. Finally, divide total distance by moving time and make sure the units match, converting minutes to hours if the question asks for miles per hour.
Hints
Use the flat part of the graph
Find the time interval where the distance does not change; that interval represents the break.
Separate moving time from total time
Subtract the break time from the total time shown on the graph to get the time spent moving.
Convert minutes to hours
To get miles per hour, convert the moving time from minutes to hours before dividing distance by time.
Desmos Guide
Read key points from the graph
From the graph, note the start point and end point . Also note the flat segment from to , which is a -minute break.
Compute moving time in hours
In Desmos, enter moving = (50-10)/60 to convert minutes to hours.
Compute average moving speed
Enter 20/moving and use the value shown as the average speed while moving (in miles per hour).
Step-by-step Explanation
Read total distance from the graph
The hiker starts at miles and ends at miles, so the total distance traveled is miles.
Find the total time spent moving
The graph is flat from to minutes, so the hiker is not moving for minutes.
Total time shown is minutes, so time spent moving is minutes.
Compute average speed while moving and convert units
Convert minutes to hours: minutes hour.
Average speed while moving is
So the hiker’s average speed while moving is 30 miles per hour.