Problem 2 · 2020 Math Kangaroo
Medium
Geometry & Measurement
spatial-reasoning
An ant used to walk 6 m in a straight line each day to go from point A to point B. One day Johnny placed an upright cylinder 1 m tall across the path. Now the ant walks along the same straight line, going up and over the cylinder and back down, as shown. How far must she walk now to get from A to B?
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Answer: A — 8 m
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Hint 1 of 2
The top of the cylinder is flat, so walking across it covers the same horizontal distance as before.
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Hint 2 of 2
Only the climbing up and back down is extra.
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Approach: account only for the extra vertical climb
- Going over the top adds the climb up (1 m) and the climb down (1 m).
- Crossing the flat top replaces the same horizontal stretch she used to walk on the ground, so that part is unchanged.
- New distance = original 6 m + 1 m + 1 m = 8 m.
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