Driven pulley speed find

This would have to be a question, asked by someone who is listed as having a bachelor of mechanical engineering, on their profile, that I can't believe they would need to ask, maybe a student who was just started at high school may ask such a question, but any engineer who ha a degree ? This is a very fundamental mechanics principle. You must of been asleep during most of your classes, or did you actually turn up for any of them ?. Did you just hand over your course fees and automatically get given your degree ?.

It is all very simple, if we look at the belt traveling around the pulleys, if we put a chalk mark on the belt, and a chalk mark on a fixed point on the machine, we would notice that the time it takes for the belt to pass the mark, for a constant speed (rpm) of the driving pulley is also constant. Now if the pulleys are the same diameter, the part of the pulley circumference on the drive pulley that the belt passes over will be the same distance as the part of the circumference the belt passes over on the driven pulley, so with no slippage of the belt the rpm of driving pulley will be the same as the driven pulley. Now starting from this point, what do you think will happen if the driven pulley is a smaller diameter than the driving pulley, a clue, circumference of a pulley is proportional to diameter ?. What do you think will happen happen if the diameter of the driven pulley is larger. Anyone with a B.E. should have no problems working this out. You could also, if this is too complex for you to work out yourself, have gotten the answer from google and not embarrassed yourself on this form stacked with many engineering professionals.