Speed, Time and Distance
- A thief is stopped by a policeman from a distance of 400 metres. When the policeman starts the chase, the thief also starts running. Assuming the speed of the thief as 5 km/h and that of policeman as 9 km/h, how far the thief would have run, before he is over taken by the policeman ?
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Distance between thief and policeman = 400 metre
Relative speed of policeman with respect to thief
= (9 – 5) kmph
= 4 kmph= 
4 × 5 
m./sec. 18 = 10 m./sec. 9
Time taken in overtaking the thief= 400 second 10/9 = 400 × 9 second 10
= 360 second
∴ Distance covered by thief
= Speed × Time= 5 × 5 × 360 metre 18
= 500 metreCorrect Option: C
Distance between thief and policeman = 400 metre
Relative speed of policeman with respect to thief
= (9 – 5) kmph
= 4 kmph= 4 × 5 m./sec. 18 = 10 m./sec. 9
Time taken in overtaking the thief= 400 second 10/9 = 400 × 9 second 10
= 360 second
∴ Distance covered by thief
= Speed × Time= 5 × 5 × 360 metre 18
= 500 metre
- Two trains start from a certain place on two parallel tracks in the same direction. The speed of the trains are 45 km/hr. and 40 km/hr respectively. The distance between the two trains after 45 minutes will be
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Relative speed = 45 – 40 = 5 kmph.
∴ Gap between trains after 45 minutes = 5 × 45 km 60
= 3.75 km.Correct Option: D
Relative speed = 45 – 40 = 5 kmph.
∴ Gap between trains after 45 minutes = 5 × 45 km 60
= 3.75 km.
- A passenger train running at the speed of 80 kms./hr leaves the railway station 6 hours after a goods train leaves and overtakes it in 4 hours. What is the speed of the goods train?
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Let the speed of goods train be x kmph.
∴ Distance covered by goods train in 10 hour = distance covered by passenger train in 4 hours
⇒ 10x = 80 × 4⇒ x = 80 × 4 = 32 kmph. 10 Correct Option: A
Let the speed of goods train be x kmph.
∴ Distance covered by goods train in 10 hour = distance covered by passenger train in 4 hours
⇒ 10x = 80 × 4⇒ x = 80 × 4 = 32 kmph. 10
- A train ‘B’ speeding with 100 kmph crosses another train C, running in the same direction, in 2 minutes. If the length of the train B and C be 150 metre and 250 metre respectively, what is the speed of the train C (in kmph)?
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Let the speed of train C be x kmph.
∴ Relative speed of B
= (100 – x ) kmph.∴ Time taken in crossing = Length of both trains Relative speed ⇒ (2/60) = 150 + 250 1000 100 − x ⇒ 1 = 2 30 5(100 − x) ⇒ 1 = 2 6 100 − x
⇒ 100 – x = 12
⇒ x = 100 – 12 = 88 kmph.Correct Option: B
Let the speed of train C be x kmph.
∴ Relative speed of B
= (100 – x ) kmph.∴ Time taken in crossing = Length of both trains Relative speed ⇒ (2/60) = 150 + 250 1000 100 − x ⇒ 1 = 2 30 5(100 − x) ⇒ 1 = 2 6 100 − x
⇒ 100 – x = 12
⇒ x = 100 – 12 = 88 kmph.
- The distance between two places A and B is 60 km. Two cars start at the same time from A and B, travelling at the speeds of 35 km/h and 25 km/h, respectively. If the cars run in the same direction, then they will meet after ( in hours)
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Let both cars meet at C after t hours.
∴ Distance covered by car A
= AC = 35t km
Distance covered by car B
= BC = 25t km
∴ AC – BC = AB = 60 km.
⇒ 35t – 25t = 60
⇒ 10t = 60⇒ t = 60 = 6 hours 10 Correct Option: C
Let both cars meet at C after t hours.
∴ Distance covered by car A
= AC = 35t km
Distance covered by car B
= BC = 25t km
∴ AC – BC = AB = 60 km.
⇒ 35t – 25t = 60
⇒ 10t = 60⇒ t = 60 = 6 hours 10
