[EricH]

Mentoring time...

Yes, I will give you the answer. But you should really understand the theory, which I will lay out first. I'll be short, I promise.

Motors have speed and torque outputs--generally, high speed and high torque aren't going to happen at the same time (at least not in the motors we're using). Gearboxes reduce speed and increase torque, or vice versa. A X:1 ratio will normally reduce speed; 1:X will increase it (but you'll need some torque to do so). As an example, spin the KOP gearbox from its output shaft and an input--there will be a difference.

Gearboxes will tend to divide speed and multiply torque by whatever their ratio is. A 5:1 gearbox will cut the available speed by a factor of 5, while increasing the torque by the same amount (CIM free speed goes to 1000 RPM from 5000 RPM). 10:1 cuts by a factor of 10 (for a CIM, that means your free speed will be somewhere around 500 RPM). And I think you get the picture for the 100:1--a CIM will end up around 50 RPM, which is mighty slow but mighty strong.

So, which gearbox will go the fastest would be the 5:1.

Side note: Motors actually output power--torque x speed, as I recall--which is why you have a hard time getting high speed and high torque at the same time.