How many revolutions will the larger wheel make .?

Question

A wheel has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller has made 21 revolutions, the number of revolutions made by the larger wheel is..?

Answer 1

Hi Roohani,

 

this is is a ratio problem, and a nice simple intro to them at that. Basically, the way these gears work is that for every one revolution of the small wheel, the large wheel will rotate some amount as well. We know that the small wheel has 6 cogs, so the large one will turn six cogs worth with each rotation, 6/14ths of a whole revolution. So we can set up the problem like this: 6/14 = x/21 where x is the number of rotations the large gear makes. We need to manipulate that ratio to simplify the problem, so we can multiple each aide by both 14 and x. That gives us 14x = 21*6, then you just need to solve for X!