Problem 29 · 2024 Math Kangaroo
Stretch
Ratios, Rates & Proportions
distance-speed-time
Anne drives from point A to point B and then immediately back to A. Benni drives from point B to point A and then immediately back to B. They drive on the same road, start at the same time, and both drive at constant speed. Anne’s speed is three times as high as Benni’s speed. They meet for the first time 15 minutes after they start. How long after the start will they meet for the second time?
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Answer: C — 30 min
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Hint 1 of 2
At the first meeting the two together have covered the whole road once, fixing the road length in their speeds.
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Hint 2 of 2
Track who turns around when; the second meeting comes after Anne (the faster one) catches Benni from behind.
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Approach: track positions through the turnarounds to the second meeting
- With speeds 3v and v meeting head-on after 15 min, the road length is 4v·15 = 60v.
- Anne reaches the far end at 20 min and turns back; Benni is still heading the same way.
- Anne then closes the 20v gap at relative speed 2v, taking 10 more min, so they meet at 30 min.
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