ANSWER: The journey which began on the twentieth day of the second month (Numbers 10:11) is called in Scripture a “three day journey.” The statement is made that verse 33 says the Israelites would journey three days to search out a place to rest, but the Bible does not say this. It rather calls the journey a three days’ journey. “What is the difference?” you might ask.
What is a three days journey? Is it a period of three complete days? Is it 72 hours? No. The Bible gives us a clear example of exactly what a three days’ journey really is. We find the answer by noticing a similar account, which mentions a particular day’s journey. Numbers 11:31 states: 31 Now a wind went out from YHWH, and it brought quail from the sea and left them fluttering near the camp, about a day’s journey on this side and about a day’s journey on the other side, all around the camp, and about two cubits above the surface of the ground.
Notice carefully that this quail was two days journey, but the children of Israel gathered them a day and a half according to Numbers 11:32a, which tells us: 32 And the people stayed up all that day, all night, and all the next day, and gathered the quail…
It took the people a day and a half to gather two days journey worth of quail. How in the world can this be done? It is possible because a day’s journey is not speaking of a twenty-four hour period, but rather a unit of measurement. In other words, one day’s journey equaled a distance traveled. Smiths Bible Dictionary has this to say concerning the phrase.
"…the day’s journey was the most usual method of calculating distances in traveling, Gen. 30:36, 31:23; Ex. 3:18, 5:3; Num. 10:33, 11:31, 33:8; Deut. 1:2; 1 Kings 19:4; 2 Kings 3:9; Jonah 3:3; 1 Macc. 5:24, 7:45; Tobit 6:1, though but one instance of it occurs in the New Testament - Luke 2:44. The ordinary day’s journey among the Jews was 30 miles; but when they traveled in companies, only ten miles. Neapolis formed the first stage out of Jerusalem according to the former and Beeroth according the latter computation. (Reference below)
According to Mr. Smith, Numbers 10:11 is meant to be taken as Israel was about to embark on a 30 mile journey. This journey could be accomplished in less than three days. Just think about the passage in regards to the quail. Not only did Israel travel the length which the quail were, but also gathered them in the process; a whole two cubits high worth of them!
We might also mention that the Bible speaks of a Sabbath day’s journey (Acts 1:12). This, too, was simply a distance or measurement, which one was allowed to travel on the Sabbath. Although this was probably an interpretive restriction, it was most likely followed by the Israelites of the first century.
I should further point out that there is nothing in the text that tells us we should believe the entire three-day’s journey was accomplished before the Sabbath of the 22nd. They could have stopped on the Sabbath, and then picked up their journey where they had left off. A sister in our local assembly gave the example of a trip to California. She stated that from Georgia to California in a car would take three days. However, if you stopped off somewhere and stayed a few days to “see the sights” it may take you five or six days to get to California. Does this mean from Georgia to California is not a journey of three days? Not at all. Keep in mind that those who believe in a continuous seven-day cycle with no interruption have no choice but to have the Israelites marching around the walls of Jericho on the Sabbath. Yet they try to use a traveling argument against lunar Sabbatarians. This is inconsistent argumentation.
1 A Dictionary of the Bible, by William Smith, 1986, pg. 740. 
Answer courtesy of Arnold Bowen’s book: Why Weekly Sabbath Days are Determined by the Moon.