## Speed, Time and Distance

#### Speed, Time and Distance

1. A train passes two persons walking in the same direction at a speed of 3 km/hour and 5km/hour respectively in 10 seconds and 11 seconds respectively. The speed of the train is
1. 28 km/hour
2. 27 km/hour
3. 25 km/hour
4. 24 km/hour

1. Let the speed of train be x kmph and its length be y km.
When the train crosses a man, it covers its own length
According to he question,

 = y = 10 (x − 3) × 5 3

⇒  18 y = 10 × 5(x –3)
⇒  18y = 50x –150   ..... (i)
 and, y = 11 (x − 5) × 5 18

⇒  18y = 55(x–5)
⇒  18y = 55x –275   .... (ii)
From equations (i) and (ii),
55x –275 = 50x–150
⇒  55x –50x = 275 – 150
⇒  5x = 125
 ⇒  x = 125 = 25 5

∴  Speed of the train = 25 kmph
Second Method :
Here, S1 = 3, S2 = 5
 t1 = 10 ,  t2 = 11 3600 3600

 Speed of train = t1S1 − t2S2 t1 − t2

 = 3 × 10 − 5 × 11 3600 3600 10 − 11 3600 3600

 = − 25 × 3600 3600 − 1

= 25 m/sec

##### Correct Option: C

Let the speed of train be x kmph and its length be y km.
When the train crosses a man, it covers its own length
According to he question,

 = y = 10 (x − 3) × 5 3

⇒  18 y = 10 × 5(x –3)
⇒  18y = 50x –150   ..... (i)
 and, y = 11 (x − 5) × 5 18

⇒  18y = 55(x–5)
⇒  18y = 55x –275   .... (ii)
From equations (i) and (ii),
55x –275 = 50x–150
⇒  55x –50x = 275 – 150
⇒  5x = 125
 ⇒  x = 125 = 25 5

∴  Speed of the train = 25 kmph
Second Method :
Here, S1 = 3, S2 = 5
 t1 = 10 ,  t2 = 11 3600 3600

 Speed of train = t1S1 − t2S2 t1 − t2

 = 3 × 10 − 5 × 11 3600 3600 10 − 11 3600 3600

 = − 25 × 3600 3600 − 1

= 25 m/sec

1. If a train, with a speed of 60 km/ hr, crosses a pole in 30 seconds, the length of the train (in metres) is :
1. 1000
2. 900
3. 750
4. 500

1. Speed of train = 60 kmph

 = 60 × 5 × 50 m/sec 18 3

&there4:  Length of train
= Speed × Time
 = 50 × 30 = 500 m 3

##### Correct Option: D

Speed of train = 60 kmph

 = 60 × 5 × 50 m/sec 18 3

&there4:  Length of train
= Speed × Time
 = 50 × 30 = 500 m 3

1. A man observed that a train 120 m long crossed him in 9 seconds. The speed (in km/hr) of the train was
1. 42
2. 45
3. 48
4. 55

1. Speed of train

 = 120 × 18 = 48 kmph 9 5

##### Correct Option: C

Speed of train

 = 120 × 18 = 48 kmph 9 5

1. In what time will a train 100 metres long cross an electric pole, if its speed be 144 km/hour ?
1. 2.5 seconds
2. 5 seconds
3. 12.5 seconds
4.  3 5 seconds 4

1. Speed of the train

 = 144 kmph = 144 × 5 = 40 m/s 18

When a train crosses a pole, it covers a distance equal to its own length.
 The required time = 100 40

 = 5 = 2 5. seconds. 2

##### Correct Option: A

Speed of the train

 = 144 kmph = 144 × 5 = 40 m/s 18

When a train crosses a pole, it covers a distance equal to its own length.
 The required time = 100 40

 = 5 = 2 5. seconds. 2

1. A 75 metre long train is moving at 20 kmph. It will cross a man standing on the platform in
1. 12 seconds
2. 14 seconds
3. 13.5 seconds
4. 15.5 seconds

1.  Speed of train (in m/s) = 20 × 5 = 50 m/sec 18 9

 Required time = 75 × 9 50

= 13.5 seconds

##### Correct Option: C

 Speed of train (in m/s) = 20 × 5 = 50 m/sec 18 9

 Required time = 75 × 9 50

= 13.5 seconds