Problem 17 · 2022 Math Kangaroo
Hard
Ratios, Rates & Proportions
distance-speed-time
A rabbit and a hedgehog enter a race against each other. The circular racecourse is 550 m long. The starting line and the finish line are the same. The speed of the rabbit is a constant 10 m/s, the speed of the hedgehog is a constant 1 m/s. They start at the same time, but the hedgehog tries to cheat by going in the opposite direction. When the two meet, the hedgehog turns around immediately and follows the rabbit. How many seconds after the rabbit does the hedgehog reach the finish line?
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Answer: A — 45
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Hint 1 of 2
Find when the two meet (closing speed) and where the hedgehog is then.
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Hint 2 of 2
After turning, the hedgehog still has to cover the rest of the loop to the finish.
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Approach: relative speed for the meeting, then finish the loop
- The rabbit finishes the 550 m loop in 550/10 = 55 s.
- Moving toward each other they close 550 m at 10+1 = 11 m/s, meeting at 50 s; the hedgehog has gone 50 m the wrong way.
- It turns and must still cover 50 m forward to the start/finish, taking 50 s more, so it finishes at 100 s.
- That is 100 - 55 = 45 s after the rabbit.
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