Problem 20 · 2021 Math Kangaroo
Medium
Ratios, Rates & Proportions
distance-speed-time
In a railway line between the cities X and Y, the trains can meet, traveling in opposite directions, only in one of its stretches, in which the line is double. The trains take 180 minutes to go from X to Y and 60 minutes to go from Y to X, at constant speeds. On this line, a train can start from X at the same instant that a train starts from Y, without them colliding during the trip. Which of the following figures represents the line?
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Answer: B
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Hint 1 of 2
The trains start together; X→Y takes 180 min and Y→X takes 60 min, so the Y-train is three times faster.
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Hint 2 of 2
They must cross exactly inside the doubled stretch — locate where they meet along the line.
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Approach: find the meeting point and place the double stretch there
- The Y-train (60 min) is three times as fast as the X-train (180 min), so after the same time it has covered three times the distance.
- They meet at the point three-quarters of the way from X to Y.
- The double (passing) section must contain that meeting point, which matches figure B.
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