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A bicycle camper rides to her first campsite on day one, then rides at a different speed to a second campsite on day two. Her average speed for the whole two days turns out to equal the plain average of her two daily speeds. What must be true of her trip?
AShe rode the same distance and the same time on both days
BShe rode different distances but the same time on both days
CShe rode the same distance but different times on both days
DShe rode different distances and different times on both days
Answer & Solution
Correct answer: B. She rode different distances but the same time on both days
1. Overall average speed is total distance over total time: (d1+d2)/(t1+t2).
2. The plain average of the two daily speeds is (d1/t1 + d2/t2)/2.
3. Setting t1 = t2 = t makes both expressions equal (d1+d2)/(2t), regardless of whether d1 and d2 differ.
4. So equal riding time each day, not equal distance, is the condition that makes the two averages match.
_Source: OpenStax Physics (CC BY 4.0), Ch 2 "Motion in One Dimension", section 2.2 Speed and Velocity_
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