Question

When two gears are mashed the revolution per minutes (rpm) are inversely proportional to the number of teeth, as show below. In one machine the rpm ratio of the larger gear to the small gear is 4:7. The small gear has 216 teet. In a second machine the large gear revolves at 500 rpm and 245 teeth. The small gear revolves at 700 rpm.
Find the number of teeth on the larger gear of the first machine?

Find the number of teeth on the small gear of the first machine?

Answer 1

Better to 'mesh' gears, not 'mash' them - that could cause damage.
Kidding aside, start by setting up the inverse variation equation for both gears,
\[y=\frac{k}{x} \rightarrow RPMs=\frac{k}{teeth}\]

Answer 2

Is that second question right? "Find the number of teeth on the small gear of the first machine?" Aren't the number of teeth on the small gear of the first machine given?

Answer 3

So what is the number of teeth on the larger gear of the first machine? and what is the number of teeth for the smaller gear?

Answer 4

For the first machine, you can use the ratio of RPM. If RPM is inversely proportional to number of teeth and the RPM ratio is 4:7::large:small, then the teeth ratio should be 7:4::large:small.

Answer 5

For the second machine, you can use the information for the large gear and the inverse variation equation to solve for k, then use that to get the number of teeth for the small gear.

Answer 6

So what is the answers been trying to figure this question out all morning

Answer 7

Are you there?

Answer 8

Is it 245 for both?

Answer 9

Like I said, you can use the ratio 7:4::large:small to find the teeth for the large gear of machine 1. Just multiply (7/4) by 216, the number of teeth for the small gear.
For machine 2, if RPM=k/teeth, and the large gear goes 500RPM with 245 teeth, then k = 500*245. Use that value of k to find the number of teeth for the small gear. Teeth=k/700RPM.

Answer 10

You can also do the same for machine 2 as for machine one by taking the ratio of RPMs 5:7::large:small.

Answer 11

you could try this method:

if rpm (r) is inversely proportional to number of teeth (t), then: \[\Large r_1\times t_1=r_2 \times t_2\]

Answer 12

Ok so is larger 378? Smaller 175?

Answer 13

@CliffSedge am I correct?

Answer 14

yes

Answer 15

That's what I got too.