I have a short answer and a long answer:
1. Convert both hex values to decimal values:
379D11 = RGB(55, 157, 11)
B03B3B = RGB(176, 59, 59)
...or, if you're comfortable computing in hex, just keep the hex values. A quick google search will provide plenty of online tools for converting.
- Average the two RGB values (and round to integer):
R: (55 + 176)/2 = 116,
G: (157 + 59)/2 = 108,
B: (11 + 59)/2 = 35,
Average = RGB(116, 108, 35)
Convert the above RGB average to HSV or HSL. There are plenty of online tools, but I tend to just use the "Edit Colors" tool of plain-old-MS Paint
Adjust the Value or Luminosity to get the amount of whiteness that looks right to you. You have your color. You just need to convert back to Hex using MS Paint or your favorite online converter.
By the time you do all the above (it took me a little less than 10 minutes), you could probably just experiment. I tend to do both. Use the above to get a ballpark figure, then adjust to suite my tastes from there.