Video: Speed as the Average Rate of Change

The table lists the distances covered in kilometers over a 15 hour hike. During which period was the average speed below 2 kilometers per hour? [A] between hour 5 and 15 [B] between hour 3 and 5

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Video Transcript

The table lists the distances covered in kilometers over a 15-hour hike. During which period was the average speed below two kilometers per hour? Was it A) between hour five and 15 or B) between hour three and five?

Before we begin this question, we need to know how to work out the speed. Well, speed is calculated by dividing the distance by the time. In this case, the average speed will be the total distance divided by the total time. Our first time period was between hour five and hour 15. How far did we travel in this time? Well, after 15 hours, we’re traveled a distance of 30 kilometers. And after five hours, we’re traveled the distance of 24 kilometers. So 30 take away 24 equals six kilometers. The amount of time that has elapsed doing this period is 10 hours; 15 take away five equals 10. Therefore, to calculate the average speed, we divide six by 10. So the average speed is 0.6 kilometers per hour or 0.6 kilometers per hour. This answer is below two kilometers per hour, which suggests that the correct answer is between hour five and hour 15.

Let’s just check the second option, just to be sure. The second option asked us to consider the time period between hour three and hour five. The distance here was six kilometers, 24 take away 18. And the time period was two hours, five take away three. Therefore, we can calculate the average speed by doing the calculation six divided by two, which equals three kilometers per hour. This is higher than two kilometers per hour that was mentioned in the question. So we know that our first answer, answer A, between five and 15 hours, was correct.

To summarize, the average speed between hour five and hour 15 was 0.6 kilometers per hour, the average speed between hour three and hour five was three kilometers per hour, therefore, the time period where the average speed was below two kilometers per hour was answer A, between hour five and 15.