## Speed, Time and Distance

#### Speed, Time and Distance

1. Two trains of equal length are running on parallel lines in the same direction at 46 km/h and 36 km/h. The faster train passes, the slower train in 36 seconds. The length of each train is :
1. 82 m
2. 50 m
3. 80 m
4. 72 m

1. Let the length of each train be x metre.
Relative speed = 46 – 36 = 10 kmph

 = 10 × 5 metre/second 18

 = 25 metre/second 9

 ∴ 2x = 36 (25/9)

 ⇒  2x = 36 × 25 = 100 9

⇒  x = 50 metre

##### Correct Option: B

Let the length of each train be x metre.
Relative speed = 46 – 36 = 10 kmph

 = 10 × 5 metre/second 18

 = 25 metre/second 9

 ∴ 2x = 36 (25/9)

 ⇒  2x = 36 × 25 = 100 9

⇒  x = 50 metre

1. A bus moving at a speed of 45 km/hr overtakes a truck 150 metres ahead going in the same direction in 30 seconds. The speed of the truck is
1. 27 km/hr
2. 24 km/hr
3. 25 km/hr
4. 28 km/hr

1. Let the speed of the truck be x kmph
Relative speed of the bus = (45 - x) kmph

 ∴   Time = Distance Relative speed

 ⇒ 30 60 × 60

 = 150 1000 (45 − x)

 ⇒ 1 = 15 120 100(45 − x)

 ⇒ 1 = 3 ⇒ (45 − x) = 18 6 (45 − x)

⇒  x = 45 – 18 = 27 kmph

##### Correct Option: A

Let the speed of the truck be x kmph
Relative speed of the bus = (45 - x) kmph

 ∴   Time = Distance Relative speed

 ⇒ 30 60 × 60

 = 150 1000 (45 − x)

 ⇒ 1 = 15 120 100(45 − x)

 ⇒ 1 = 3 ⇒ (45 − x) = 18 6 (45 − x)

⇒  x = 45 – 18 = 27 kmph

1. Two trains travel in the same direction at the speed of 56 km/h and 29 km/h respectively. The faster train passes a man in the slower train in 10 seconds. The length of the faster train (in metres) is
1. 100
2. 80
3. 75
4. 120

1. Relative speed = 56 – 29 = 27 kmph

 = 27 × 5 = 15 m/sec 18 2

∴  Distance covered in 10 seconds
 = 15 × 10 = 75 m 2

Hence, length of train = 75 m.

##### Correct Option: C

Relative speed = 56 – 29 = 27 kmph

 = 27 × 5 = 15 m/sec 18 2

∴  Distance covered in 10 seconds
 = 15 × 10 = 75 m 2

Hence, length of train = 75 m.

1. Two trains are running with speed 30 km/hr and 58 km/hr in the same direction. A man in
the slower train passes the faster train in 18 seconds. The length (in metres) of the faster train is :
1. 70
2. 100
3. 128
4. 140

1. Relative speed = (58 – 30) km/hr

 = 28 × 5 m/sec. 18

 = 70 m/sec. 9

 ∴   Length of train = 70 × 18 9

= 140 metres

##### Correct Option: D

Relative speed = (58 – 30) km/hr

 = 28 × 5 m/sec. 18

 = 70 m/sec. 9

 ∴   Length of train = 70 × 18 9

= 140 metres

1. A constable follows a thief who is 200 m ahead of the constable. If the constable and the thief run at speed of 8 km/hour and 7 km/hour respectively, the constable would catch the thief in
1. 10 minutes
2. 12 minutes
3. 15 minutes
4. 20 minutes

1. The constable and thief are running in the same direction
∴   Their relative speed = 8 – 7 = 1km.

 = 1 × 5 m/sec. 18

 ∴ Required time = 200 5 18

 = 200 × 18 = 720 sec 5

 = 720 minutes = 12 minutes 60

##### Correct Option: B

The constable and thief are running in the same direction
∴   Their relative speed = 8 – 7 = 1km.

 = 1 × 5 m/sec. 18

 ∴ Required time = 200 5 18

 = 200 × 18 = 720 sec 5

 = 720 minutes = 12 minutes 60