What is the magic time and temperature for stewing meat and vegetables?

Question

I made an oxtail stew in the crockpot/slow-cooker today, and 6 hours later I added the vegetables (carrots, onions, celery) which was also one hour before dinner time. Unfortunately, two hours later, the vegetables were still tough and crunchy, which earned me a reprimand from my wife for dinner being late. :-( The reason why I didn't add in the vegetables from the beginning is because I didn't want the vegetables to be overcooked and too soft.

Motivated by the desire to earn praise rather than rebuke from my darling, what is the right time and temperature for stewing meat and vegetables? Is the solution to first sweat the vegetables?

What I have found so far:

1. According to Rose Prince (see link), the magic time and temperature for a beef stew recipe is 7 hours at 80°C = 175°F
2. According to What is the lowest possible temperature for stewing meat?, vegetables should be done at 80°C-95°C

While point (1.) tells me how long to cook the meat, I'm not sure based on point (2.) whether that will leave the vegetables undercooked or overcooked.

Answer 1

If you are going to wait until an hour before serving you definitely have to sweat the vegetables, you could also add them to the stew earlier, like half way through the cooking of the meat. In a pinch I have also put vegetables in some water with seasoning in the microwave after about 4 or 5 minutes, the will be softer, then add to the stew. I also don't think that adding the vegetables with the meat for the whole cooking time is a problem, the vegetables take on all that flavor that the meat gives up.