A train having a length of 110 meter is running at a speed of 60 kmph. In what time, it will pass a man who is running at 6 kmph in the direction opposite to that of the train?
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Solution
distance = 110 m
Relative speed = 60 + 6 = 66 kmph (Since both the train and the man are in moving in opposite direction) = 66 × meter per second = .
Time = distance/speed = 110/(110/6) = 6 seconds
Two stations P and Q are 110 km apart on a straight track. One train starts from P at 7 a.m. and travels towards Q at 20 kmph. Another train starts from Q at 8 a.m. and travels towards P at a speed of 25 kmph. At what time will they meet ?
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Solution
Assume both train meet after x hours after 7 am
Distance covered by train starting from P in x hours = 20x km
Distance covered by train starting from Q in (x – 1) hours = 25 (x – 1)
Total distance = 110
= 20x + 25(x – 1) = 110
= 45x = 135
= x = 3
Means they meet after 3 hours after 7 am, i.e. they meet at 10 am.
Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. the faster train passes the slower train in 36 seconds. The length of the each train is:
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Solution
Let the length of each train be x meters.
Then, distance covered = 2x metres.
Relative speed = (46 – 36) km/hr =
∴ meter
A train is traveling at 96 kmph. It crosses another train having half of its length traveling in opposite direction at 84 kmph, in 24 seconds. It also passes a railway platform in 90 seconds. What is the length of the platform?
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Solution
Speed of train 1 = 96 kmph
Let the length of train 1 = 2x meter
Speed of train 2 = 84 kmph
Length of train 2 = x meter (because it is half of train 1’s length)
Distance = 2x + x = 3x
Relative speed = 96 + 84 = 180 kmph = 180 ×
Time = 24s
Distance/time = speed = = 50
⇒ x = 50 × 24/3 = 400 meter
length of the first train = 2x = 800 meter
Time taken to cross the platform = 90 s
Speed of train 1 = 96 kmph =
Distance = 800 + y where y is the length of the platform
= 800 + y = 90 ×
= y = 1600 meters.
A train moves past a police post and a flyover 420 m long in 9 sec and 30 sec respectively. What is the speed of the train?
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Solution
Let the length of the train be x meters and its speed be y m/sec.
Then, = 9 ⇔ x = 9y.
Now, = y
⇔ 30y = x +420
⇒ 30y = 9y +420
⇒ 21y = 420 ⇒ y = 20
Speed = 20 m/sec =
A 270 meters long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
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Solution
Relative speed = (120 + 80) km/hr=
Let the length of the other train be x meters.
Then, = ⇔ x = 230 meter
A jogger is running at 9 kmph alongside a railway track with 240 meters ahead of the engine of a 120 meters long train. The train is running at 45 kmph in the same direction. How much time does it take for the train to pass the jogger ?
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Solution
Distance to be covered = 240 + 120 = 360 m
Relative speed = 36 km/hr = 36 ×
Time = distance/speed = = 36 seconds.
A train having a length of mile , is traveling at a speed of 75 mph. It enters a tunnel miles long. How long does it take to pass the tunnel?
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Solution
Total distance = + = miles
Speed = 75 mph
Time = hr = hr = minutes = 3 minutes
A train runs at the speed of 144 kmph and crosses a 550 m long platform in 35 seconds. What is the length of the train?
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Solution
Speed = 144 kmph = = 40 m/s
Distance covered = 550 + x where x is the length of the train
Time = 35 s
550 + x = 35 × 40 = 1400 m
x = 1400 – 550 = 850 m
A train overtakes two persons walking along a railway track. The first person walks at 13.5 km/hr and the other walks at 16.2 km/hr. The train needs 16.8 and 17 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?
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Solution
Let x is the length of the train in meter and y is its speed in kmph
Dividing 1 by 2
⇒ 16.8y – 16.8 × 13.5 = 17y – 17 × 16.2
0.2y = 17 × 16.2 – 16.8 × 13.5
⇒ 0.2y = 275.4 – 226.8 = 48.6
⇒ y = 243 km/hr