Patna Express leaves Delhi at 10:00 AM and reaches Patna at 7:00 PM the same day. Delhi Express leaves Patna at 2:00 PM and reaches Delhi at 1:00 AM on the next day. Both trains travel on the same route in opposite directions. At what time do they meet?
04:45 PM
Let the distance between Delhi and Patna be \(D\).
Patna Express takes 9 hours (10:00 AM to 7:00 PM), so its speed \(= \frac{D}{9}\). Delhi Express takes 11 hours (2:00 PM to 1:00 AM), so its speed \(= \frac{D}{11}\).
By 2:00 PM, the Patna Express (running since 10:00 AM, 4 hours) has covered \(4 \times \frac{D}{9} = \frac{4D}{9}\), leaving a gap of \(\frac{5D}{9}\) between the two trains.
From 2:00 PM both trains move toward each other with combined speed \(\frac{D}{9} + \frac{D}{11} = \frac{20D}{99}\).
Time to meet after 2:00 PM \(= \frac{5D/9}{20D/99} = \frac{5}{9} \times \frac{99}{20} = 2.75\) hours \(= 2\) hours 45 minutes.
Adding this to 2:00 PM gives 4:45 PM. Hence, the trains meet at 04:45 PM.
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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:
