Problem 9 · 2025 Math Kangaroo
Medium
Ratios, Rates & Proportions
proportiondistance-speed-time
Three turtles are competing in a 10 km race. Each of them moves at a constant speed. When the first turtle finishes the competition, the second has completed 14 of the distance and the third has completed 15 of the distance. How far is the third turtle from the finish line when the second turtle finishes the race?
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Answer: B — 2 km
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Hint 1 of 2
The turtles move at steady speeds, so the distance each has covered tells you their speed ratio.
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Hint 2 of 2
When the 2nd turtle finishes, its distance has grown by the same factor as the 3rd turtle’s.
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Approach: scale the third turtle’s distance by the same factor
- When the 1st finishes 10 km, the 2nd has done 1/4 of 10 = 2.5 km and the 3rd has done 1/5 of 10 = 2 km.
- For the 2nd turtle to reach 10 km, time must be multiplied by 10 ÷ 2.5 = 4.
- In that same time the 3rd turtle goes 2 × 4 = 8 km.
- So the 3rd turtle is 10 − 8 = 2 km from the finish.
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