Problem 24 · 2025 Math Kangaroo
Stretch
Ratios, Rates & Proportions
distance-speed-time
Anurag lives 1 km from his school and sets off at the same time every day. Walking, he travels at 4 km/h; cycling, he travels at 15 km/h. When he walks, he arrives 5 minutes before school starts. How many minutes before school starts does he arrive if he cycles?
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Answer: E — 16
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Hint 1 of 2
Find how long the 1 km walk takes and how long the 1 km ride takes.
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Hint 2 of 2
Cycling saves the time difference, so add that saving to the 5 minutes he already had to spare.
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Approach: compare travel times and the fixed start moment
- Walking 1 km at 4 km/h takes 15 minutes; cycling 1 km at 15 km/h takes 4 minutes.
- He leaves at the same moment, so cycling gets him there 15 − 4 = 11 minutes earlier than walking.
- Walking he is 5 minutes early, so cycling he is \(5 + 11 = 16\) minutes early, which is (E).
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