Thursday, November 7, 2013

Vayetzei- Rate of Speed: What's your walking speed?

"And [Lavan] put a distance of three days between himself and Jacob; and Jacob tended Lavan's flock that remained" ~Bereishit 30;36

"So [Jacob] fled- he and all he had; he arose and crossed the river and he set his direction toward Mount Gilead. It was told to Lavan on the third day that Jacob had fled. So he took his brethren with him and he chased after him a seven-days' journey, and caught up with him on Mount Gilead." ~Bereishit 31;21-23

Rashi here explains the timing and distance. To begin with, Lavan was already 3 days away from Jacob, as we are told in 30;36. Therefore, when Jacob left, it took the informer 3 days to reach Lavan with the news of Jacob's departure. Rashi then explains that "a seven-days' journey" is for us to understand that, while Jacob was 7 days ahead of Lavan (3 days to begin with, plus 3 days of travel forward while the informer was traveling in the other direction to tell Lavan, plus the day on which Lavan reached him), Lavan actually covered this distance to reach Jacob on his first day of travel- 4 days after Jacob left.

Rate: a quantity, amount, or degree of something measured per unit of something else (merriam-webster.com)

Basically, when comparing any two different measurements to each other, you have a rate. Common examples from our daily lives are miles per hour (speed), or dollars per pound (cost). When calculating with a rate, it is helpful to calculate a base rate, which tells you the amount of one measurement per one single unit of the other measurement.

If we look at how far Jacob and Lavan each traveled, and the length of time that it took each of them to travel their respective distances, then we can calculate the rate of speed that each of them was traveling. 

From the text and Rashi's commentary, we know that Jacob traveled for a total of 4 days, and Lavan traveled for a total of 1 days. Now for the distance that each man traveled:

Based on the information that we have from the text and from Rashi, let's assume that the distance that they were each traveling was from the general Padan-Aram/Haran area to Mount Gilead. On a current map, we can use the map coordinates for Harran and for Ramoth-Gilead to approximate the distance that they traveled. Although it won't calculate travel distance, if we plot the coordinates onto a map and estimate the distance between the two locations, it's approximately 300 mi between the two locations. 

Now, let's consider that Jacob (and his wives and children and sheep) traveled those 300 miles in 4 days, and Lavan chased after him and traveled the 300 miles in 1 day. 
7-days journey- If the Torah assumes that this journey should have taken 7 days, then 300 miles in 7 days is roughly 43 miles each day. Assuming 12 hours of walking time each day, the standard travel rate would be about 3.5 m/h (miles per hour).
Jacob- 300 miles was the 7 day journey. If Jacob was only traveling for 4 days (note that he was 3 days away from Lavan's flocks), we can subtract about 120 miles from his trip (3 days x 40 miles each day). This means that he traveled 300-120= 180 miles. These 180 miles divided into 4 days means that he traveled 45 miles per day. This is equal to just under 2 m/h if he didn't stop to rest or sleep, but just walked 24 hours a day straight for the 4 days. To be more realistic, let's assume that he walked a total of 12 hours each day- to allow for sleeping at night and resting with children. 45 miles divided into 12 hours means that they were walking at a leisurely rate of 3.75 m/h.
Lavan- He traveled 300 miles in a single day. Since we know that he was chasing after Jacob to catch him right away, and he was running with just his brothers, let's assume that they ran until they caught up to Jacob. If it took him a full 24 hours, then he was running at a rate of 12.5 m/h. If we assume that he needed to stop at nightfall, and could, at most, travel 12 hours in the day, then he was traveling at a rate of 25 m/h. 

Before you scoff at these rates, we could say that they were actually traveling by camel (it does specifically say this for Jacob- Bereishit 31;17), which is able to reach speeds of 40 m/h and sustain a speed of up to 25 m/h (ref. wikipedia).

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