Speed, Time and Distance
 If a man reduces his speed to 2/3, he takes 1 hour more in walking a certain distance. The time (in hours) to cover the distance with his normal speed is :

 2
 1
 3
 1.5

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Since man walks at 2/3 of usual speed, time taken will be 3/2 of usual time.
∴ 3 of usual time = usual time + 1 hour. 2 ⇒ 3 − 1 of usual time = 1 2
⇒ usual time = 2 hours.Correct Option: A
Since man walks at 2/3 of usual speed, time taken will be 3/2 of usual time.
∴ 3 of usual time = usual time + 1 hour. 2 ⇒ 3 − 1 of usual time = 1 2
⇒ usual time = 2 hours.
 Two trains of equal length are running on parallel lines in the same direction at 46 km/hour and 36 km/hour. The faster train passes the slower train in 36 seconds. The length of each train is

 72 m
 80 m
 82 m
 50 m

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Let the length of each train be x metre.
Relative speed = (46 – 36) kmph = 10 kmph= 10 × 5 m./sec. 18 = 25 m./sec. 9 ∴ 2x = 36 25 9 ∴ 2x = 36 × 25 = 100 9 ⇒ x = 100 = 50 metre 2 Correct Option: D
Let the length of each train be x metre.
Relative speed = (46 – 36) kmph = 10 kmph= 10 × 5 m./sec. 18 = 25 m./sec. 9 ∴ 2x = 36 25 9 ∴ 2x = 36 × 25 = 100 9 ⇒ x = 100 = 50 metre 2
 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 ?

 400 metre
 600 metre
 500 metre
 300 metre

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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

 2.5 km.
 2.75 km.
 3.7 km.
 3.75 km.

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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?

 32 kmph
 50 kmph
 45 kmph
 64 kmph

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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