To draw a graph of Ann's speed in mph in terms of time in hours, we need to find the rate at which her distance traveled changes over time. This can be calculated by finding the slope of the line connecting each pair of points on the graph.
Using the provided points on the graph (0,0), (1,3), (4,5), (7,5), and (10,10), we can calculate the speed at each time point by dividing the change in distance by the change in time.
Speed (mph) = Change in distance / Change in time
For the given points, the calculated speeds are as follows:
At t = 0 hours to t = 1 hour:
Speed (mph) = (3 - 0) / (1 - 0) = 3 mph
At t = 1 hour to t = 4 hours:
Speed (mph) = (5 - 3) / (4 - 1) = 2/3 mph
At t = 4 hours to t = 7 hours:
Speed (mph) = (5 - 5) / (7 - 4) = 0 mph
At t = 7 hours to t = 10 hours:
Speed (mph) = (10 - 5) / (10 - 7) = 5/3 mph
Based on these calculations, we can plot the four speeds on the graph, using the corresponding time points.
The graph would look like this:
^
|
|
Speed (mph)| 3
| /
| /
| /
+-----------------
1 4 7 10 Time (hours)
Note that the speed is constant at 3 mph between 0 and 1 hour, then decreases gradually to 0 mph between 4 and 7 hours, and finally increases to 5/3 mph between 7 and 10 hours.