Problem 25 · 2020 Math Kangaroo
Stretch
Ratios, Rates & Proportions
Number Theory
distance-speed-time
Jonas was driving his car and saw the following information on the car display: speed 90 km/h, distance travelled 116.0 km, and time 21h00min. Jonas kept driving at the same speed, and that same night he noticed that the four-digit sequence showing the distance travelled was the same four-digit sequence showing the time. At what time did this happen?
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Answer: D — 22h10min
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Hint 1 of 2
At 90 km/h he gains 90 km each hour (1.5 km per minute); update both the distance and the clock together.
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Hint 2 of 2
Find the moment when the four digits of the distance match the four digits of the time.
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Approach: advance distance and time together
- At 90 km/h the distance climbs by 1.5 km per minute from 116.0 km at 21h00.
- After 70 minutes (at 22h10) the distance is 116 + 90·(70/60) = 221.0 km.
- The distance digits 2–2–1–0 match the time 22h10 exactly.
- So it happened at 22h10min, choice D.
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