Problem 21 · 2024 Math Kangaroo
Stretch
Algebra & Patterns
distance-speed-time
A kangaroo jumps up a mountain and back down again on the same path. Going up, it covers 1 metre per jump. Going down, it covers 3 metres per jump. In total it jumped 2024 times. How many metres did it cover in total?
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Answer: D — 3036
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Hint 1 of 2
The climb up and the climb down cover the same height H, but with different jump sizes.
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Hint 2 of 2
Write the number of up-jumps and down-jumps in terms of H and set their sum to 2024.
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Approach: express jumps via height, solve, then double the height
- Up: H metres at 1 m/jump needs H jumps. Down: H metres at 3 m/jump needs H/3 jumps.
- Total jumps: H + H/3 = 4H/3 = 2024, so H = 1518 m.
- Distance covered is up + down = 2H = 3036 metres.
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