Problem 15 · 2017 Math Kangaroo
Hard
Ratios, Rates & Proportions
proportionratio
A belt system is made up of wheels A, B and C, which rotate without sliding. B rotates 4 times around, while A turns 5 times around, and B rotates 6 times around, while C turns 7 times around. The circumference of C is 30 cm. How big is the circumference of A?
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Answer: B — 28 cm
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Hint 1 of 2
Wheels joined by a belt move the same length of belt, so turns × circumference is equal.
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Hint 2 of 2
Chain the A–B relation to the B–C relation.
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Approach: equal belt length means revolutions are inversely proportional to circumference
- Wheels joined by a belt cover the same belt length, so each wheel's turns × circumference is the same on the link.
- For B and C: 6 × (circumference of B) = 7 × 30, so the circumference of B is 35 cm.
- For A and B: 5 × (circumference of A) = 4 × 35, so the circumference of A is 28 cm, choice B.
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