Chukat- Two Approaches to Distance Traveled as Related to Rate of Speed

This week I would like to follow-up on my post from Parshat Chukat last year. In last year's post, I looked at the distance that the Children of Israel traveled in Bamidbar Chapters 20-21. Using an estimated route, I calculated that they traveled approximately 312.5 miles in this final section of their wandering in the desert.

"The Children of Israel, the entire assembly, arrived at the Wilderness of Zin in the first month and the people settled in Kadesh. Miriam died there and she was buried there." ~Numbers 20:1

From Midrash, we learn that these two chapters take place in the final year of the wandering. We learn in this first statement that we are beginning this section from the first month of this final year of wandering. Throughout the course of these 2 chapters, we have Miriam's death with 30 days of mourning and Aaron's death with 30 days of mourning. This means that out of the final full year of wandering, the Children of Israel had at most 10 months of travel time. While we know that there were periods of traveling and periods of encampment, we can still calculate an average rate of travel in terms of miles traveled per month. We could break it down further to calculate average miles traveled per day or even per hour. Let's remember that when you look at an average rate, it doesn't mean that you are traveling consistently over the whole time period, but if you broke up your entire travel so that you were traveling equal distances each hour, day, week, or month, this is how much you would have traveled in that space of time.

Back in Parshat Vayetzei, I first looked at Rate of Speed, where you express how fast or slow something or someones covers a distance by comparing the distance covered to the amount of time that it takes to cover the distance. This comparison is expressed as a ratio. So, if I travel 30 miles over the course of 1 hour, then my rate of speed would be 30 miles per hour (30mi/1hr or 30mph). If I travel 100 miles in 2 hours, then my rate could be expressed as 100mi/2hr or reduced as 50mph (since 100/2 reduces to 50/1).

Using this understanding of rate of speed, how could we look at the travel speed of the Children of Israel during the end of their wandering in the desert?

Rate of travel per month: 

Based on the estimates that I calculated last year, the distance traveled was 312.5 miles, and using my timeline logic above, they had 10 months of potential travel time.

Therefore, the rate per month would have been: 

312.5mi/10mo

This reduces to an average of 31.25mi/1mo or 31.25 miles per month

Follow-up:

Following this thinking-

*you can compare how many days would have been in the 10 months of travel time, and then calculate the estimated rate of miles per day

*how many hours would have been in those 10 months? what would the average rate of miles per hour have been?

*would the miles per hour calculation be a realistic estimate? Think about what this would mean for travel time and rest time during each day or week. How might you adjust this calculation to account for resting time each day (don't forget stopping for Shabbat)? How might you adjust the original calculations to allow for estimated periods of encampment based on the timeline that we're given in the parsha?

An alternate approach:
Looking at it from a different angle, if we estimate a reasonable rate of speed for their travel, how many hours/days/weeks/months would they have needed to be traveling and how much time would they have had for their periods of encampment?

*What does this mean? What would be a reasonable estimate for the amount of distance they were able to travel in an hour? a day? a week? a month? By quantifying some of these rates, how might their travel have lined up with the information that is provided in the parsha? How long would it have taken them to get between their different stops where they requested and were denied permission to cross through other lands? How might you create an estimated timeline of their travel using all of this information?

*Personal connection: Think about it similar to planning a road trip- how much mileage do you have to cover? What stops or activity locations might you be planning, and what are the distances between the stops? What is a reasonable rate of speed for your travel? How long will it take you between each stop? Can you fit your trip within a given timeframe or do you need more time to reasonably make your full trip?

Note: It is important to remember that this information is all hypothetical, since we don't have day by day or month by month itemizations of travel time or encampment periods. Additionally, my calculations from last year were merely estimates as well. That being said, thinking about the situation within this context can help students create a semblance of understanding around what the Children of Israel might have actually been going through in their travels- offering a realistic link to this "story".