SOLUTION: The speed of a gear varies directly as the number of teeth it contains. If a gear with 10 teeth rotates at 240rpm, with what speed would a gear with 18 teeth revolve under the same

Question 320596: The speed of a gear varies directly as the number of teeth it contains. If a gear with 10 teeth rotates at 240rpm, with what speed would a gear with 18 teeth revolve under the same conditions?

I'm getting 2 answers not sure which one is right 240x10=2400/18=133
240x18=4320/10=432
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let x = # of teeth and y = rpm

So "If a gear with 10 teeth rotates at 240rpm", then and . Because "The speed of a gear varies directly as the number of teeth it contains", this means that . Plug in and to get and solve for 'k' to get . So giving us the equation

Now we want to know the rpm when 18 teeth are involved. So now . Plug this into the equation above to get meaning that a 18 tooth gear will spin at 432 rpm.

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Alternate Solution:

"If a gear with 10 teeth rotates at 240rpm, with what speed would a gear with 18 teeth revolve under the same conditions? " means that . Basically, the ratio of the number of teeth to the rpm is the same.

Start with the given ratio

Multiply both sides by x

Multiply both sides by 240

Multiply

Divide both sides by 10

Reduce

So our answer is which means that a gear with 18 teeth will rotate at 432 rpm. So we get the same answer.

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