TL;DR -- 11

There are many factors involved, which makes this a difficult question to answer with a single number. But let's try.

The standard accepted answer for Roman legionaries is 20 miles/day (nice discussion here: http://www.romanarmytalk.com/thread-5631.html ), which would give you 180/20 = 9 days, with an 5-hr marching day a speed of 4 mph. This is fully loaded with gear, and having to build a fort in the evening. This is a standard, not a forced march. But those cats didn't have to forage, and, well ... hostiles would be smart to dodge them. How does that affect things, hmm...

According to the accepted answer here ( How long per day does it take to forage/hunt for food? ) in relatively bountiful terrain you can get away with 3 hrs/day for hunting/foraging.

We also need to set aside some time for dodging enemies. This is wildly variable, depending on amount of cover, how sparse the enemies are, and so on. I'll suggest that just to get some numbers on the table we assume two hours of cowering under a bush every day.

So that gives us 10 busy hours per day, leaving plenty of time for making camp, having character-establishing scenes, and getting some rest.

So, if you accept this teetering stack of assumptions, you still can make 20 miles/day and make it in 9 days. Throw in an extra day for crossing the river, and another for some emergency.

I'm going to say 11 days, including a little bit of buffer.

TL;DR -- 11 days

There are many factors involved, which makes this a difficult question to answer with a single number. But let's try.

The standard accepted answer for Roman legionaries is 20 miles/day (nice discussion here: http://www.romanarmytalk.com/thread-5631.html ), which would give you 180/20 = 9 days, with an 5-hr marching day a speed of 4 mph. This is fully loaded with gear, and having to build a fort in the evening. This is a standard, not a forced march. But those cats didn't have to forage, and, well ... hostiles would be smart to dodge them. How does that affect things, hmm...

According to the accepted answer here ( How long per day does it take to forage/hunt for food? ) in relatively bountiful terrain you can get away with 3 hrs/day for hunting/foraging.

We also need to set aside some time for dodging enemies. This is wildly variable, depending on amount of cover, how sparse the enemies are, and so on. I'll suggest that just to get some numbers on the table we assume two hours of cowering under a bush every day.

So that gives us 10 busy hours per day, leaving plenty of time for making camp, having character-establishing scenes, and getting some rest.

So, if you accept this teetering stack of assumptions, you still can make 20 miles/day and make it in 9 days. Throw in an extra day for crossing the river, and another for some emergency.

I'm going to say 11 days, including a little bit of buffer.