Speed, Time and Distance
- Two trains are running in opposite direction with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, the speed of each train (in km/hour) is
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Let the speed of each train be x kmph.
Their relative speed
= x + x = 2x kmphTime taken = Total length of trains Relative Speed = 12 60 × 60 240 × 1 = 1000 2x = 1 = 120 300 1000x x = 300 × 120 = 36 1000
The required speed = 36 kmph.Correct Option: C
Let the speed of each train be x kmph.
Their relative speed
= x + x = 2x kmphTime taken = Total length of trains Relative Speed = 12 60 × 60 240 × 1 = 1000 2x = 1 = 120 300 1000x x = 300 × 120 = 36 1000
The required speed = 36 kmph.
- Two trains 140 m and 160 m long run at the speed of 60 km/ hour and 40 km/hour respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is :
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Total length of trains
= 140 + 160 = 300 m.
Relative speed = 60 + 40 = 100 kmph= 100 × 5 m/sec. 18 or 250 m/sec. 9
∴ Time taken to cross each other= 300 250 9 = 300 × 9 = 10.8 sec. 250 Correct Option: B
Total length of trains
= 140 + 160 = 300 m.
Relative speed = 60 + 40 = 100 kmph= 100 × 5 m/sec. 18 or 250 m/sec. 9
∴ Time taken to cross each other= 300 250 9 = 300 × 9 = 10.8 sec. 250
- Two trains start from stations A and B and travel towards each other at speed of 50 km/hour and 60 km/hour respectively. At the time of their meeting, the second train has travelled 120 km more than the first. The distance between A and B is :
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Let train A start from station A and B from station B.
Let the trains A and B meet after t hours.
∴ Distance covered by train A in t hours = 50t
Distance covered by train B in t hours = 60t km
According to the question,
60t – 50t = 120⇒ t = 120 = 12 hours. 10
∴ Distance AB = 50 × 12 + 60 ×
12 = 600 + 720 = 1320 km
Second Method :
Here, a = 60, b = 50, d = 120Distance between A and B = 
a + b 
× d a − b = 60 + 50 × 120 60 − 50 = 110 × 120 = 1320 km 10 Correct Option: C
Let train A start from station A and B from station B.
Let the trains A and B meet after t hours.
∴ Distance covered by train A in t hours = 50t
Distance covered by train B in t hours = 60t km
According to the question,
60t – 50t = 120⇒ t = 120 = 12 hours. 10
∴ Distance AB = 50 × 12 + 60 ×
12 = 600 + 720 = 1320 km
Second Method :
Here, a = 60, b = 50, d = 120Distance between A and B = a + b × d a − b = 60 + 50 × 120 60 − 50 = 110 × 120 = 1320 km 10
- Two trains are moving on two parallel tracks but in opposite directions. A person sitting in the train moving at the speed of 80 km/hr passes the second train in 18 seconds. If the length of the second train is 1000 m, its speed is
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Let the speed of second train be x m/s.
80 km/h = 80 × 5 m/s 18
According to the question1000 = 18 x + 80 × 5 18
⇒ 1000 = 18x + 400∴ x = 600 m/s 18 = 600 × 18 km/h = 120 km/h 18 5 Correct Option: B
Let the speed of second train be x m/s.
80 km/h = 80 × 5 m/s 18
According to the question1000 = 18 x + 80 × 5 18
⇒ 1000 = 18x + 400∴ x = 600 m/s 18 = 600 × 18 km/h = 120 km/h 18 5
- Two trains 105 metres and 90 metres long, runs at the speed of 45 km/hr and 72 km/hr respectively, in opposite directions on parallel tracks. The time which they take to cross each other, is
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Length of both trains
= 105 + 90 = 195 m.
Relative speed = (45 + 72) = 117 kmph= 117 × 5 or 65 m/sec. 18 2 ∴ Time taken = 195 65 2 = 195 × 2 = 6 seconds 65 Correct Option: B
Length of both trains
= 105 + 90 = 195 m.
Relative speed = (45 + 72) = 117 kmph= 117 × 5 or 65 m/sec. 18 2 ∴ Time taken = 195 65 2 = 195 × 2 = 6 seconds 65
