Problem 28 · 2017 Math Kangaroo
Stretch
Ratios, Rates & Proportions
distance-speed-time
Two runners are training at the same time on a 720 m long, round running track. They run with constant speed in opposite directions. The first runner needs four minutes for one lap, the second five minutes. How many metres does the second runner run between two consecutive meetings of the two runners?
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Answer: E — 320
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Hint 1 of 2
Running opposite ways, the two runners' speeds add when finding how fast the gap to the next meeting closes.
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Hint 2 of 2
Find the time between meetings, then multiply by the slower runner's speed.
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Approach: closing speed gives the meeting interval
- Speeds: 720/4 = 180 m/min and 720/5 = 144 m/min; closing speed = 180 + 144 = 324 m/min.
- They meet every 720 ÷ 324 minutes; in that time the second runner covers 144 × 720/324.
- That equals 320 m.
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