Two trains, A and B, start simultaneously from stations Delhi and Mumbai respectively towards each other on parallel tracks. After meeting, train A takes 16 hours to reach Mumbai, and train B takes 9 hours to reach Delhi. If train A's speed is 60 km/h, what is the length of train B (in meters), given that it crosses a pole in 18 seconds?
400
Using the property of trains meeting: if after meeting, train A takes \(t_A\) hours and train B takes \(t_B\) hours to reach their respective destinations, then \(\frac{v_A}{v_B} = \sqrt{\frac{t_B}{t_A}}\).
Here \(t_A = 16\) h, \(t_B = 9\) h, so \(\frac{v_A}{v_B} = \sqrt{\frac{9}{16}} = \frac{3}{4}\).
Given \(v_A = 60\) km/h: \(\frac{60}{v_B} = \frac{3}{4}\), so \(v_B = 80\) km/h.
Convert train B's speed to m/s: \(80 \times \frac{1000}{3600} = \frac{200}{9}\) m/s.
Train B crosses a pole in 18 seconds, so its length \(= \frac{200}{9} \times 18 = 400\) m.
Hence, the length of train B is 400 metres.
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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:
