Problem 22 · 2014 Math Kangaroo
Stretch
Ratios, Rates & Proportions
distance-speed-time
The king travels with his messengers at 5 km/h from his castle to his summer residence. Every hour he sends one messenger back to the castle at 10 km/h. What is the difference in arrival times between two messengers who arrive at the castle one after the other?
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Answer: D — 90 min
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Hint 1 of 2
Work out when the first two messengers each set off and how far from the castle they start.
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Hint 2 of 2
Each messenger travels back at 10 km/h; find its arrival time, then subtract two consecutive arrivals.
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Approach: find each messenger's start distance and return time
- After 1 hour the king is 5 km out; that messenger rides back 5 km at 10 km/h, taking 0.5 h, so it arrives 1 + 0.5 = 1.5 h after departure.
- After 2 hours the king is 10 km out; that messenger rides back 10 km at 10 km/h, taking 1 h, so it arrives 2 + 1 = 3 h after departure.
- The gap between these two arrivals is 3 − 1.5 = 1.5 h = 90 min (and every later pair gives the same 90 minutes).
- The difference is 90 minutes.
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