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2012 Math Kangaroo

Problem 20

Problem 20 · 2012 Math Kangaroo Medium
Ratios, Rates & Proportions distance-speed-time

At an airport there is a “rolling pavement” which is 500 m long and transports people with a speed of 4 km/h. Anna and Peter step onto the rolling pavement at the same time. While Peter is standing still, Anna continues to walk with a speed of 6 km/h. How big is Anna’s head start on Peter when she leaves the rolling pavement after 500 m?

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Answer: E — 300 m
Show hints
Hint 1 of 2
Add Anna's walking speed to the belt's speed to get her ground speed.
Still stuck? Show hint 2 →
Hint 2 of 2
Find how long Anna takes for 500 m, then see how far Peter (moving with the belt) gets in that time.
Show solution
Approach: distance = speed × time
  1. Anna's ground speed is 4 + 6 = 10 km/h; Peter just rides the belt at 4 km/h.
  2. Anna covers 500 m = 0.5 km in 0.5 ÷ 10 = 0.05 h.
  3. In 0.05 h Peter travels 4 × 0.05 = 0.2 km = 200 m, so Anna's lead is 500 − 200 = 300 m.
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