A train A passes a fixed pole in 24 seconds. The same train completely crosses another train B of length 150 m coming from the opposite direction in 20 seconds. Train B’s speed is 54 km/h. Find the length and the speed of train A.
900 m and 135 km/h
Let the length of train A be \(L\) metres and its speed be \(v\) m/s.
Passing a pole: \(L = 24v\).
Speed of train B = 54 km/h = \(54\times\tfrac{5}{18}=15\) m/s.
Trains move in opposite directions, so relative speed = \(v+15\) m/s and combined distance to cross = \(L+150\) m.
Hence \(\dfrac{L+150}{v+15}=20\ \Rightarrow\ L+150 = 20v+300\).
Substituting \(L=24v\): \(24v+150 = 20v+300 \Rightarrow 4v = 150 \Rightarrow v = 37.5\) m/s.
So speed of A = \(37.5\times\tfrac{18}{5}=135\) km/h and \(L=24\times 37.5=900\) m.
Hence, train A is 900 m long with a speed of 135 km/h.
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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:
