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Two persons are walking in the same direction as a train. The first person walks at a speed of 3 km/h, and the second person walks at a speed of 5 km/h. The train overtakes the first person in 36 seconds and the second person in 40 seconds, where each time is measured from the moment the front of the train reaches the person to the moment the last carriage clears the person. What is the length of the train in meters?
A. 150 m
B. 160 m
C. 180 m
D. 200 m
E. 220 m
A. 150 m
B. 160 m
C. 180 m
D. 200 m
E. 220 m
11 Mar 2026, 08:44
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Official Solution:
Two persons are walking in the same direction as a train. The first person walks at a speed of 3 km/h, and the second person walks at a speed of 5 km/h. The train overtakes the first person in 36 seconds and the second person in 40 seconds, where each time is measured from the moment the front of the train reaches the person to the moment the last carriage clears the person. What is the length of the train in meters?
A. 150 m
B. 160 m
C. 180 m
D. 200 m
E. 220 m
Let \(l\) be the length of the train in km and let \(s\) be the speed of the train in km/h.
36 seconds \(= \frac{36}{3600}\) hour \(= \frac{1}{100}\) hour.
40 seconds \(= \frac{40}{3600}\) hour \(= \frac{1}{90}\) hour.
Use distance \(= \) relative speed \(* \) time, since the train must cover its full length relative to the person:
\(l = (s - 3) * \frac{1}{100}\).
\(l = (s - 5) * \frac{1}{90}\).
So:
\(\frac{s - 3}{100} = \frac{s - 5}{90}\).
\(s = 23\).
Then:
\(l = \frac{23 - 3}{100} = \frac{1}{5}\) km \(= 200\) m.
Answer: D
Two persons are walking in the same direction as a train. The first person walks at a speed of 3 km/h, and the second person walks at a speed of 5 km/h. The train overtakes the first person in 36 seconds and the second person in 40 seconds, where each time is measured from the moment the front of the train reaches the person to the moment the last carriage clears the person. What is the length of the train in meters?
A. 150 m
B. 160 m
C. 180 m
D. 200 m
E. 220 m
Let \(l\) be the length of the train in km and let \(s\) be the speed of the train in km/h.
36 seconds \(= \frac{36}{3600}\) hour \(= \frac{1}{100}\) hour.
40 seconds \(= \frac{40}{3600}\) hour \(= \frac{1}{90}\) hour.
Use distance \(= \) relative speed \(* \) time, since the train must cover its full length relative to the person:
\(l = (s - 3) * \frac{1}{100}\).
\(l = (s - 5) * \frac{1}{90}\).
So:
\(\frac{s - 3}{100} = \frac{s - 5}{90}\).
\(s = 23\).
Then:
\(l = \frac{23 - 3}{100} = \frac{1}{5}\) km \(= 200\) m.
Answer: D
