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2023 Math Kangaroo

Problem 24

Problem 24 · 2023 Math Kangaroo Stretch
Ratios, Rates & Proportions distance-speed-timetotal-then-divide

An ant walks along the sides of an equilateral triangle (see diagram). Its speed is 5 cm/min along the first side, 15 cm/min along the second and 20 cm/min along the third. What is the average speed, in cm/min, at which the ant walks once around the whole triangle?

Figure for Math Kangaroo 2023 Problem 24
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Answer: C — 18019
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Hint 1 of 2
Average speed is total distance divided by total time, not the average of the three speeds.
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Hint 2 of 2
Let each side be length L; add the three times L/5, L/15, L/20 and divide 3L by that.
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Approach: average speed = total distance / total time
  1. Let each side have length L; the times on the sides are L/5, L/15 and L/20.
  2. Total time = L(1/5 + 1/15 + 1/20) = L(12+4+3)/60 = 19L/60.
  3. Average speed = 3L ÷ (19L/60) = 180/19 cm/min.
  4. So the answer is 180/19 (C).
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