Hi Cal.
I'm afraid my answer is a bit like 'how long is a piece of string'.
The burn time for any given cylinder can vary massively, and depends on several factors, which is why I cannot answer you properly!
As an average, you will be looking at approx 90 minutes running time for a 250 cart. I chose A 250 cart, as it would give the stove more stability on rough ground. Things to bear in mind could be (and ignore this if you know it all already) that when you are boiling water for a bru, you are going to be using a very narrow pot (your vango mug), so you will only need to have the stove on half power to boil your water. If you have the stove on full power, it will not boil any faster, as the small base of the pot will only accept so much heat exchange, but you will waste lots of gas, which will simply be pushed out to the sides of your pot (and heat the handles so they are too hot to touch). The outside air temp and water temp will also play a huge part in boiling times, as will the wind speed. It is worth remembering that the boil times quoted by the manufacturers have no similarity to those out in the field...Unless of course your field is at 20 degrees c with no wind at all, and your water is at 20 degrees c too!. Luckily the stove you have is less affected by wind than a lot of other cannister top stoves, so you will not lose too much heat to the wind.
Will you be using a wind shield? A good wind shield can knock two mins off your boiling time, so you save quite a lot of gas (you can cook on lower settings too). I prefer a wind shield to cover some of the pot too, and not just the area to the side of the flame, as this speeds boiling time. You may know that the gas vapour comes from the cylinder at very cold temperatures (-73 degrees c for butane) and this is why frost forms on cylinders during cooking. This lowered temperature affects the ability of the gas to vaporise in the cylinder, and so reduces the output of the flame (which is why 'butane only' cylinders do not work properly below 8 C). A good wind shield will will help to trap some heat from the flame and keep the cylinder warm, so increasing flame size.
Once your water is boiling, you can either turn off the stove (hardly rocket science was it !), or if you want to cook some dehydrated food, you could then put the pot into a pot cosy, so your food will continue to cook, while using no extra gas. For example, if you cooked some dried pasta, and two pot noodles, you could potentially save 20 mins of gas by using a pot cosy. This is not purely to save money and the earth's resources, but means you carry less gas (i.e. weight) on longer trips.
So, if you keep your flame turned down to a level where is will still just keep the water boiling (longer boiling times do not always mean more gas used here), and use a good wind shield, then look to get at least 90 mins from a 250 gas cart. As you are looking to perhaps keep your stove and gas in the pot, one other tip is that when you finish boiling you water, just pop the pot back over the stove until all the water residue in it dries out. This will prevent your stove, or the bare metal base of the gas cart leaving rust in your pot. This makes the pot easier to clean, and stops any damage to any non stick coatings it may have.
