Answers:
- Problem 1) 25 miles
- Problem 2) 3 hours
- Problem 3) They are cycling the fastest from 10:00 a.m. to 10:30 a.m.
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Explanations:
- The vertical axis, aka y axis, tells us how many miles are traveled. The highest it goes is y = 25, which is the number of miles traveled. They reach this marker at 1:00 p.m.
- The timespan from 10:00 a.m. to 12:00 p.m. is 2 hours (since 12-10 = 2). Then from 12:00 p.m. to 1:00 p.m. is an extra hour. In total, they traveled for 2+1 = 3 hours.
- They are cycling the fastest when the distance/time graph is steepest. Recall that the slope represents the speed when x is the time and y is the distance. This is because speed = distance/time. Apply the slope formula to the various different pieces and you should find the slope is largest from 10:00 a.m. to 10:30 a.m. The speed here is 20 mph. The next section has a speed of 10 mph. They then take a rest from 11:30 a.m. to 12:00 noon due to the flat horizontal portion here. The last section has a speed of 5 mph.
