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
A train is to cover 370 km at a uniform speed. After running 100 km, the train could run at a speed 5 km/h less than its normal speed due to some technical fault. The train got delayed by 36 minutes. What is the normal speed of the train, in km/h?
A train travelling at 36 km/h crosses a pole in 25 seconds. How much time (in seconds) will it take to cross a bridge 250 m long?
A train covers 450 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less to cover the same distance. How much time will it take to cover 315 km at its usual speed?
A train crosses a pole in 12 sec, and a bridge of length 170 m in 36 sec. Then the speed of the train is:
The ratio of the speeds of two trains is 2 : 7. If the first train runs 250 km in 5 hours, then the sum of the speeds (in km/h) of both the trains is:
