## Speed, Time and Distance

#### Speed, Time and Distance

1. 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 :
1. 2
2. 1
3. 3
4. 1.5

1. 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.

1. 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
1. 72 m
2. 80 m
3. 82 m
4. 50 m

1. 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

1. 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 ?
1. 400 metre
2. 600 metre
3. 500 metre
4. 300 metre

1. 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

##### Correct 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

1. 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
1. 2.5 km.
2. 2.75 km.
3. 3.7 km.
4. 3.75 km.

1. 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.

1. 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?
1. 32 kmph
2. 50 kmph
3. 45 kmph
4. 64 kmph

1. 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