briks123 wrote:

I get C.

The circumference of of the big circle is 96pi and the circumference of the small circle is 24pi. Their gears are traveling at the same rate, so we can pick a number, say 8pi/hr because 8pi is the LCF. Then the big circle's rate is 1/12 revolutions per hour and the small circle's rate is 1/3 revolutions per hour.

Letting d1 be the distance that the large gear is moving and d2 be the distance that the small gear is moving, we want to find out when d1+d2=192pi (ie 96pi+96pi).

So for the big wheel: (1/12)*t=d

And for the small wheel: (1/3)*t= 192pi-d

Solving for d, we get that t=12d and t=576pi-3d. This means 12d=576pi-3d. Which means 15d=576pi. Which means d=38.4pi.

briks,

you are only one to respond - much appreciated!

but this was the same problem i had with their solution also. when it is given "same rate", my conclusion was "same rpm", not "same distance/hr", since we are dealing with rotational (not linear) speed. have u seen a similar problem in a reliable math text which takes the linear speed?

but for this assumption (which changes the entire solution), the rest of your solution is valid.

expert or knowledgeable person on this topic, plz comment/clarify...