Final answer:
For a bicycle camper whose average speed over two days equals the average of her speeds each day, the distance traveled each day must have been the same. Consequently, the time taken to travel those distances each day must also be the same.
Step-by-step explanation:
If a bicycle camper rides from her starting point to her first campsite one day and continues to a second campsite the next day, and her average speed for the two days equals the average of her speeds each day, then the distance traveled each day must have been the same. When the distances (d1, d2) are the same, the average speed over the two days can be the simple arithmetic mean of the two daily speeds (v1, v2).
To elaborate, the average speed for the entire journey is the total distance divided by the total time taken. If the total distance for both days is the same, and the average speed equals the arithmetic mean of the two speeds, then the time taken each day (t1, t2) must also be the same. This is because speed is directly proportional to distance when time is held constant, and for the overall average speed to equal the arithmetic mean of two speeds, the weight (time in this case) given to each speed must be equal.