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

Algebra ->  Equations -> 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      Log On


   

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) About Me  (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 x=10 and y=240. Because "The speed of a gear varies directly as the number of teeth it contains", this means that y=kx. Plug in x=10 and y=240 to get 240=k%2810%29 and solve for 'k' to get k=240%2F10=24. So k=24 giving us the equation y=24x



Now we want to know the rpm when 18 teeth are involved. So now x=18. Plug this into the equation above to get y=24%2818%29=432 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 10%2F240=18%2Fx. Basically, the ratio of the number of teeth to the rpm is the same.


10%2F240=18%2Fx Start with the given ratio


%2810%2F240%29%2Ax=18 Multiply both sides by x


10%2Ax=18%2A240 Multiply both sides by 240


10%2Ax=4320 Multiply


x=4320%2F10 Divide both sides by 10


x=432 Reduce



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