What's highest speed at which I could possibly travel?

Solution 1:

Running

Normal running speed is capped at 520 Hammer units per second (a Hammer unit is 1/16 of a foot). It became this when the Scout's Baby Face Blaster was released, up from its former limit of 400 (I think) Hammer units per second. This is a hard cap and only one ability will let you go over that speed...

Side Note: "Normal" 100% running speed is 300 Hammer Units per second.

DemoMan Charging

The charge speed is exempt from the normal speed limit and instead maxes out at 750 Hammer units per second. It will go slower than that if the Demo is using a Skullcutter), but never faster. The length of the charge is normally 1 second, but the Claidheamh Mòr will increase this to 1.5 seconds.

The shield will have a 12 second recharge time, 6 second if using the Persian Persuader.

So... here's a quick chart of the speesd after 1, 2, 7, and 8 seconds. 8 being chosen because it's after the second Persian Persuader charge.

Scout vs. Demo speeds

As you can see, a stock Scout will barely outrun the fastest demo over time, but a Baby Face Blaster Scout can outrun everything else.

However, the fastest movement speed in the game? Taking a short range critical Direct Hit rocket while jumping. It's powerful enough to send you all the way between pl_upward's A and B points in seconds. Of course, only a Dead Ringer Spy can actually survive that since it does 450 damage.

Solution 2:

The speed you have posted is the highest speed, not counting explosive-jumping. Of course, in regards to "standard running speed", a Scout

with BFB at 100% boost = 173% base moving speed
under Concheror effect or Disciplinary Whip effect +40% of base (120%)
Round Won +10% of base (120%)
under Crit-A-Cola effect = +25%

would clearly beat out the demo.

Here's a nice infographic that shows running speeds: http://thomaspark.me/project/tf2speeds/

You'll notice that obviously the demo has the fastest burst running speed, but long-term, the scout wins, hands down, every single time.

Solution 3:

Trimping (otherwise known as charge jumping or charge ramping) allows you to travel at speeds above 2100 hammer units per second if you strafe in the air,. That's three times faster than a charging Demoman on the ground. This is by far the fastest way you can travel that isn't very situational.