Ok, to answer my own question in order to further build my understanding - this is how i would have explained it to myself.
Starting with the foundational:
1. Distance = Speed * Time
Distance is directly proportional to both Speed and Time. Direct proportionality rule x = ky.
Speed is inversely proportional to time. Indirect proportionality rule is x = k/y
Logically, as your speed increases and time remains constant, you will travel further.
Or if your speed increases, and distance remains the same, then your time will decrease.
Why do we hold certain constants, I assumed it was because based on the proportionality rules, because we're trying to isolate for changes in just 2 objects at a time rather than all 3 simultaneously. This is an important point to remember, because without holding one variable constant, these proofs are not true.
Example:
John travels 10km in 2 hour. He travels at 5km/h.
If john doubles his speed, he will now travel at 10km/h.
The ratio of S:T before was 10:2 (5:1) and now it is 10:1. So they have an inversely proportionate relationship.
If we were comparing 2 objects speed, I can prove that the RATIOS of the two objects speed are inversely proportional to their time as well.
E.g. Object A travels D distance with TimeA(Ta) and SpeedA (Sa). Ta = D/Sa
Object B travels D distance with TimeB (Tb) and SpeedB (Sb). Tb = D/Sb
Ta:Tb = (D/Sa):(D:Sb) = Sb/Sa
here's an example i pulled from source site:
LINKExample 1: If I travelled at 3/4th of my average speed and reached 25 minutes late, what is the time that I usually take to reach my destination?
the ratio of speed is 3:4 the ratio if time is 4:3. This means that for every 3 minutes I would usually take to get to my destination, I took 1 more minute today. I have 25 extra minutes so that's 25*3 = 75 minutes regularly and today I took 100 minutes.
i hope this helps somebody else as well