Question

When two gears are mashed, the revolutions per minute (rpm) are inversely proportional to the number of teeth, as shown below. In one machine the rpm ratio of the large gear to the small gear is 1:3. the small gear has 44 teeth. In a second machine the large gear revolves at 200 rpm and has 423 teeth. The small gear revolves at 900 rpm

rpm of large gear/rpm of small gear= # of teeth on small gear/ teeth on large gear

Answer 1

There is no question here.

Answer 2

I need help finding the number of teeth on the large gear of the first machine and then also finding the number of teeth on the small gear of the second machine

Answer 3

I have no idea how to even begin to find the answer

Answer 4

In one machine the RPM ratio of the LARGE gear TO the SMALL gear is 1:3.
rpm_large / rpm_small = 1 / 3
Since rpm is inversely proportional to the number of teeth:
rpm_large / rpm_small = teeth_small / teeth_large ----- (1)
The small gear has 44 teeth.
Plug in the numbers into (1):
1 / 3 = 44 / teeth_large
cross multiply:
teeth_large = 44 x 3 = 132 teeth on the larger gear.

Answer 5

You want to try the second part?

Answer 6

200/900?

Answer 7

That is the ratio on the left. You have correctly found rpm_large / rpm_small = 200 / 900

Now do the right hand side.

Answer 8

so the first machine has 132 teeth on the large gear?

Answer 9

Yes, the first machine has 132 teeth on the large gear.

Answer 10

3.5/423?

Answer 11

rpm_large = 200
rpm_small = 900
teeth_large = 423
teeth_small = ?

Plug into the formula: rpm_large / rpm_small = teeth_small / teeth_large
200 / 900 = teeth_small / 423
multiply both sides by 423
200 * 423 / 900 = teeth_small
teeth_small = 94

Answer 12

that makes more sense how you wrote it out. I was confused

Answer 13

alright.

Answer 14

so you did 200*423 which = 84600 and you took that and divided it by 900? and that is how you got 94?

Answer 15

Yes.

Answer 16

ok thank you so much

Answer 17

you are welcome.