2 cogged wheels, one having 32 cogs and other 54 cogs,work together.if second wheel turns 160 times in three-quaters of a min,how often does the other wheel turn in 8 sec???
let's pretend that a "cog" is a unit of distance
so in 160 revs the second wheel went 160(54) or 8640 cogs
in that same time the first wheel had to do 8640/32 or 270 revolutions
it did that in 45 seconds, so it went
270/45 or 6 revolutions per second
---> so in 8 seconds it went 48 revs
or to totally cut through the fog:
second wheel did 160 revs is 45 sec
---> 32/9 revs/second
The speed would be inversely proportional to the number of cogs, that is, the more the cogs the less the speed.
R/(32/9) = 54/32
= (32/9)(54/32)
R = 6 revs/second
so in 8 seconds it would go 49 revs