Sandy recently made a 210-mile car trip, starting from home at noon. The graph at right shows how Sandy’s distance from home (measured in miles) depends on the number of hours after noon. Make up a story that accounts for the four distinct parts of the graph. In particular, identify the speed at which Sandy spent most of the afternoon driving. ​

There is no one set answer as you could get creative to have multiple variations; however, they should all have the same key features.

One such story could be this:

Sandy starts driving at noon and her average speed is 30 mph. After 1 hour, she realizes that she may not make it in time, so she increases her speed to 60 mph. Or perhaps that traffic lightened up to allow her to drive faster. By 2 PM, she stops for gas and food. She also decides to rest for an hour. At 3 PM is when she starts driving again, and does so at an average speed of 60 mph like the second leg of the trip. She finally arrives at her destination at 5 PM, which is 5 hours after she started.

Sandy spent the most time driving 60 mph which consists of the second and fourth parts of the trip. If you ignore the rest period, then it would be the second and third driving parts of the trip.

If you're wondering how I got the speed values, I used the slope formula

m = (y2-y1)/(x2-x1)

So for instance, the slope through (0,0) and (1,30) is

m = (y2-y1)/(x2-x1)

m = (30-0)/(1-0)

m = 30

Showing the first leg of the trip she had an average speed of 30 mph.

The flat part of the graph has slope 0 to indicate that Sandy isn't driving at all during that period (since her mileage y value isn't going up).

the answer is 31.27mph

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