My car might need to do 3 mph (miles per hour) in heavy traffic, and 120 mph on an autobahn. That is a factor of one to forty.
The engine would stall or get jumpy if I tried to use in at less than 1000 rpm (revolutions per minute), and blow up if I ran it over 6000 rpm. That is a factor of one to six.
What a gearbox does is to use gear wheels in different combinations to adjust parts of those speeds so they can both work in their respective ranges.
As an extra, reverse gear puts an extra cog in the mix. Using an odd number of cogs makes the output run in the opposite direction.
Take a look at a pedal cycle. The cogs are driven by a chain instead of direct contact, but the principle is the same. The rotary speed of a big cog wheel pulls more teeth per revolution that a smaller cog. So the rider’s feet on the pedals turn the wheel by different amounts, and the place where the wheel touches the ground moves faster.
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