The way I was taught is similar, but I feel it is easier and shorter. Imagine a car that only goes 10 ft/sec. If you go straight forward, after one second, you've moved ten feet. Now if you decide to go at a 45 degree angle, you're still only going 10 ft/sec, but you cant have gone forward ten feet because you're also going to the right (or left, doesn't matter) some amount of feet. Consequently, if you're moving forward through time at 10 units/units (sec/sec? I dunno, it's weird) and decide to move in the xyz dimensions, your speed through the t dimension must decrease. Now imagine that if you were standing still, you would be going through time at the speed of light (Again, units are wonky when you do this). If you tried to move through xyz at the speed of light, you would have to stop moving through time, since the speed of light is the limit to your speed. And going faster than the speed of light in X would be impossible, because there's not enough energy. (Maybe going FTL in x would make tou go backwards in time? I'm not sure of there's a consensus on that.)
PS. Typed this on my phone in the car. Forgive stupud mistakes?