Speed, Time and Distance
- Two trains start from stations A and B and travel towards each other at speeds of 50 kmph and 60 kmph 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 both trains meet after t hours.
∴ Distance = speed × time
∴ 60t – 50t = 120
⇒ 10t = 120 ⇒ t = 12 hours
∴ Required distance
= 60t + 50t
= 110t = 110 × 12
= 1320 kmCorrect Option: C
Let both trains meet after t hours.
∴ Distance = speed × time
∴ 60t – 50t = 120
⇒ 10t = 120 ⇒ t = 12 hours
∴ Required distance
= 60t + 50t
= 110t = 110 × 12
= 1320 km
- Two trains of equal length are running on parallel lines in the same direction at the rate of 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is
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Length of each train = x metre
Relative speed = 46 – 36 = 10 kmph= 
10 × 5 
m/sec 18 = 25 m/sec 9 ∴ Time taken in crossing = Length of both trains Relative speed ⇒ 36 = 2x 25 9 ⇒ 2x = 36 × 25 = 100 9 ⇒ x = 100 = 50 metre 2 Correct Option: A
Length of each train = x metre
Relative speed = 46 – 36 = 10 kmph= 10 × 5 m/sec 18 = 25 m/sec 9 ∴ Time taken in crossing = Length of both trains Relative speed ⇒ 36 = 2x 25 9 ⇒ 2x = 36 × 25 = 100 9 ⇒ x = 100 = 50 metre 2
- A thief steals a car at 1.30 p.m. and drives it off at 40 km/hr. The theft is discovered at 2 p.m. and the owner sets off in another car at 50 km/hr. He will overtake the thief at
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Distance covered by the thief in half an hour
= 1 × 40 = 20 km 2
Relative speed of car owner
= 50 – 40 = 10 km∴ Required time = Difference of distance Relative speed = 20 = 2 hours 10
i.e. at 4 p.m.Correct Option: B
Distance covered by the thief in half an hour
= 1 × 40 = 20 km 2
Relative speed of car owner
= 50 – 40 = 10 km∴ Required time = Difference of distance Relative speed = 20 = 2 hours 10
i.e. at 4 p.m.
- Two trains 125 metres and 115 metres in length, are running towards each other on parallel lines, one at the rate of 33 km/hr and the other at 39 km/hr. How much time (in seconds) will they take to pass each other from the moment they meet ?
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Relative speed
= (33 + 39) kmph
= 72 kmph= 72 × 5 m/sec. 18
= 20 m/sec.∴ Time taken in crossing = Length of both trains Relative speed = 125 + 115 = 240 20 20
= 12 secondsCorrect Option: C
Relative speed
= (33 + 39) kmph
= 72 kmph= 72 × 5 m/sec. 18
= 20 m/sec.∴ Time taken in crossing = Length of both trains Relative speed = 125 + 115 = 240 20 20
= 12 seconds
- A goods train starts running from a place at 1 P.M. at the rate of 18 km/hour. Another goods train starts from the same place at 3 P.M. in the same direction and overtakes the first train at 9 P.M. The speed of the second train in km/hr is
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Distance covered by the first goods train in 8 hours = Distance covered by the second goods train in 6 hours.
⇒ 18 × 8 = 6 × x⇒ x = 18 × 8 = 24 kmph 6 Correct Option: A
Distance covered by the first goods train in 8 hours = Distance covered by the second goods train in 6 hours.
⇒ 18 × 8 = 6 × x⇒ x = 18 × 8 = 24 kmph 6
