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
Eight railway stations A, B, C, D, E, F, G and H are connected either by two-way passages or one-way passages. One-way passages are from C to A, E to G, B to F, D to H, G to C, E to C and H to G. Two-way passages are between A and E, G and B, F and D, and E and D.
If the route between G and C is closed, which one of the following stations need not be passed through while travelling from H to C?
A daily train is to be introduced between station A and station B starting from each end at 6 AM and the journey is to be completed in 42 hours. What is the number of trains needed in order to maintain the Shuttle Service?
A train with a uniform speed passes a 122 meters long platform in 17 seconds and a 210 meters long bridge in 25 seconds. The speed of the train is:
How long does a train 153 meters long running at the rate of 90 kmph take to cross a bridge 622 meters in length?
A train passes a 360 metre long platform in 40 seconds and a man standing on the platform in 16 seconds. The speed of the train is:
