A train overtakes two runners moving in the same direction at speeds of 5 km/h and 7 km/h, passing them completely in 18 seconds and 20 seconds, respectively. What is the length of the train (in metres)?
100
Let the train's speed be \(v\) km/h and its length be \(L\) metres.
Relative speed with the 5 km/h runner is \((v-5)\) km/h, so \(L = (v-5) \times \frac{5}{18} \times 18 = (v-5) \times 5\) metres (converting 18 s to hours and simplifying).
Relative speed with the 7 km/h runner is \((v-7)\) km/h, so \(L = (v-7) \times \frac{5}{18} \times 20\).
Equating the two expressions: \((v-5) \times 18 = (v-7) \times 20\), which gives \(18v - 90 = 20v - 140\), so \(2v = 50\), hence \(v = 25\) km/h.
Length: \(L = (25-5) \times \frac{5}{18} \times 18 = 20 \times 5 = 100\) metres.
Hence, the length of the train is 100 metres.
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Important Questions from Problem on Trains
A train, 250 m long, passes a railway platform 200 m long, in 45 s with a uniform speed. What is the time (in seconds) taken by the train to pass a man cycling in the direction of the train at a speed of 6 km/h?
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The distance between two stations A and B is 700km. A train covers the journey from A to B at a speed of 80 km/h and returns back to A with a uniform speed of 65 km/h. The average speed of train during the whole journey, is closes to:
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