## Speed, Time and Distance

#### Speed, Time and Distance

1. How much time does a train, 50 m long, moving at 68 km/ hour take to pass another train, 75 m long, moving at 50 km/hour in the same direction ?
1. 5 seconds
2. 10 seconds
3. 20 seconds
4. 25 seconds

1. Both trains are moving in the same direction.
∴  Their relative speed
= (68 – 50) kmph = 18 kmph

 = 18 × 5 = 5 m/sec 8

Total length = 50 + 75 = 125 m
 ∴   Required time = Total length Relative speed

 = 125 = 25 seconds. 5

##### Correct Option: D

Both trains are moving in the same direction.
∴  Their relative speed
= (68 – 50) kmph = 18 kmph

 = 18 × 5 = 5 m/sec 8

Total length = 50 + 75 = 125 m
 ∴   Required time = Total length Relative speed

 = 125 = 25 seconds. 5

1. A constable is 114 metres behind a thief. The constable runs 21 metres and the thief runs 15
metres in a minute. In what time will the constable catch the thief ?
1. 19 minutes
2. 18 minutes
3. 17 minutes
4. 16 minutes

1. The gap of 114 metre will be filled at relative speed.

 Required time = 114 minutes 21 − 15

 = 114 = 19 minutes 6

##### Correct Option: A

The gap of 114 metre will be filled at relative speed.

 Required time = 114 minutes 21 − 15

 = 114 = 19 minutes 6

1. A moving train, 66 metres long, overtakes another train of 88 metres long, moving in the same direction in 0.168 minutes. If the second train is moving at 30 km/hr, at what speed is the first train moving ?
1. 85 km/hr.
2. 50 km/hr.
3. 55 km/hr.
4. 25 km/hr.

1. Suppose the speed of first train be x kmph
Speed of second train = 30 kmph

 = 3 × 1000 = 500 m per min. 60

∴  According to question
 Total Distance Relative speed

 = (66 + 88) = 0.168 x − 500

 ⇒ 154 = 0.168 x − 500

⇒  0.168x – 84 = 154
⇒  0.168x = 238
 ⇒  x = 238 0.168

 = 238 × 1000 m per minute 168

 = 238 × 1000 × 3 kmph 168 50

= 85 kmph

##### Correct Option: A

Suppose the speed of first train be x kmph
Speed of second train = 30 kmph

 = 3 × 1000 = 500 m per min. 60

∴  According to question
 Total Distance Relative speed

 = (66 + 88) = 0.168 x − 500

 ⇒ 154 = 0.168 x − 500

⇒  0.168x – 84 = 154
⇒  0.168x = 238
 ⇒  x = 238 0.168

 = 238 × 1000 m per minute 168

 = 238 × 1000 × 3 kmph 168 50

= 85 kmph

1. A thief is noticed by a policeman from a distance of 200m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km./hr and 11 km./hr respectively. What is the distance between them after 6 minutes ?
1. 100 m
2. 190 m
3. 200 m
4. 150 m

1. Relative speed of police
= 11 – 10 = 1 kmph

 = 5 m/sec 18

 ∴  Distance decreased in 6 minutes = 5 × 6 × 60 18

= 100 m
∴  Distance remained between them = 200–100 = 100 m

##### Correct Option: A

Relative speed of police
= 11 – 10 = 1 kmph

 = 5 m/sec 18

 ∴  Distance decreased in 6 minutes = 5 × 6 × 60 18

= 100 m
∴  Distance remained between them = 200–100 = 100 m

1. The speeds of three cars are in the ratio of 1 : 3 : 5. The ratio among the time taken by these cars to travel the same distance is
1. 3 : 5 : 15
2. 15 : 3 : 5
3. 15 : 5 : 3
4. 5 : 3 : 1

1.  Speed ∝ 1 Time

 ∴   Required ratio of time = 1 : 1 : 1 3 5

 = 15 : 1 × 15 : 1 × 15 3 5

= 15 : 5 : 3

##### Correct Option: C

 Speed ∝ 1 Time

 ∴   Required ratio of time = 1 : 1 : 1 3 5

 = 15 : 1 × 15 : 1 × 15 3 5

= 15 : 5 : 3