## Speed, Time and Distance

#### Speed, Time and Distance

1. A train is moving at a speed of 80 km/h and covers a certain distance in 4.5 hours. The speed of the train to cover the same distance in 4 hours is
1. 100 km/h
2. 70 km/h
3. 85 km/h
4. 90 km/h

1. Distance = Speed × Time
= 80 × 4.5 = 360 km

 ∴   Required speed = 360 = 90 kmph. 4

##### Correct Option: D

Distance = Speed × Time
= 80 × 4.5 = 360 km

 ∴   Required speed = 360 = 90 kmph. 4

1. Two trains are running 40 km/hr and 20 km/hr respectively in the same direction. The fast train completely passes a man sitting in the slow train in 5 seconds. The length of the fast train is
1.  23 2 m 9
2. 27 m
3.  27 7 m 9
4. 23 m

1. Relative speed = 40 – 20 = 20 km/hour

 = 20 × 5 m/sec. 18

 ∴   Length of the faster train = 20 × 5 × 5 metres 18

 = 250 = 27 7 metres 9 9

##### Correct Option: C

Relative speed = 40 – 20 = 20 km/hour

 = 20 × 5 m/sec. 18

 ∴   Length of the faster train = 20 × 5 × 5 metres 18

 = 250 = 27 7 metres 9 9

1. A policeman goes after a thief who has 100 metres start, if the policeman runs a kilometre in 8 min, and the thief a km in 10 min, the distance covered by thief before he is over-powered is
1. 350 m
2. 400 m
3. 320 m
4. 420 m

1.  Relative speed = 1000 − 1000 8 10

 = 5000 − 4000 = 1000 m/minute 40 40

 ∴  Required time = 100 1000 40

 = 4000 = 4 m/minute 1000

 ∴   Distance covered by the thief = 1000 × 4 10

= 400 metres

##### Correct Option: B

 Relative speed = 1000 − 1000 8 10

 = 5000 − 4000 = 1000 m/minute 40 40

 ∴  Required time = 100 1000 40

 = 4000 = 4 m/minute 1000

 ∴   Distance covered by the thief = 1000 × 4 10

= 400 metres

1. A boy started from his house by bicycle at 10 a.m. at a speed of 12 km per hour. His elder brother started after 1 hr 15 mins by scooter along the same path and caught him at 1.30 p.m. The speed of the scooter will be (in km/hr)
1. 4.5
2. 36
3.  18 2 3
4. 9

1. Let the speed of Scooter be x Distance covered by cycling in

 3 1 hours = Distance covered by scooter in 2

 2 1 hours 4

 ⇒  12 × 7 = x × 9 2 4

 ⇒  x = 12 × 7 × 2 9

 = 56 = 18 2 kmph 3 3

##### Correct Option: C

Let the speed of Scooter be x Distance covered by cycling in

 3 1 hours = Distance covered by scooter in 2

 2 1 hours 4

 ⇒  12 × 7 = x × 9 2 4

 ⇒  x = 12 × 7 × 2 9

 = 56 = 18 2 kmph 3 3

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 km 500 m
2. 2 km 750 m
3. 3 km 750 m
4. 3 km 250 m

1. Relative speed = 45– 40 = 5 kmph

 ∴  Required distance = 5 × 45 km 60

 = 15 km = 3 km 750 4

##### Correct Option: C

Relative speed = 45– 40 = 5 kmph

 ∴  Required distance = 5 × 45 km 60

 = 15 km = 3 km 750 4