Problem 25 · 2019 Math Kangaroo
Stretch
Ratios, Rates & Proportions
proportiondistance-speed-time
Two points are marked on a circular disc that rotates about its centre. The outer point is 3 cm further away from the centre than the inner point, and it moves 2.5 times as fast as the inner point. How big is the distance between the outer point and the centre of the circular disc?
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Answer: E — 5 cm
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Hint 1 of 2
On a spinning disc, speed is proportional to distance from the centre.
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Hint 2 of 2
If the outer radius is r and the inner is r − 3, then r/(r − 3) = 2.5.
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Approach: speed proportional to radius
- Speed ∝ radius, so (outer radius)/(inner radius) = 2.5.
- With inner = r − 3 and outer = r: r = 2.5(r − 3) ⇒ 1.5r = 7.5 ⇒ inner = 2.
- Outer radius = 2 + 3 = 5 cm.
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