Problem 18 · 2012 Math Kangaroo
Stretch
Ratios, Rates & Proportions
ratioproportion
Four cogs are connected to each other as shown in the picture. The first has 30 teeth, the second 15, the third 60 and the fourth 10. How many turns will the last cog make for each full turn of the first cog?
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Answer: A — 3
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Hint 1 of 2
Connected gears pass the same number of teeth; the in-between gears do not change the first-to-last result.
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Hint 2 of 2
Compare only the first gear's teeth with the last gear's teeth.
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Approach: teeth passed are equal; compare first and last
- One full turn of the first gear moves 30 teeth along the chain of gears.
- Those same 30 teeth pass the last gear, which has only 10 teeth.
- So the last gear turns 30 / 10 = 3 times (the middle gears do not matter).
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