## Speed, Time and Distance

#### Speed, Time and Distance

1. A moving train passes a platform 50 metres long in 14 seconds and a lamp-post in 10 seconds. The speed of the train is
1. 24 km/hr.
2. 36 km/hr.
3. 40 km/hr.
4. 45 km/hr.

1. Suppose length of train be x
According to question

 x + 50 = x 14 10

⇒  14x = 10x + 500
⇒  4x = 500
 ⇒  x = 500 = 125 m 4

Therefore, speed
 = 125 × 18 = 45 kmph 10 5

##### Correct Option: D

Suppose length of train be x
According to question

 x + 50 = x 14 10

⇒  14x = 10x + 500
⇒  4x = 500
 ⇒  x = 500 = 125 m 4

Therefore, speed
 = 125 × 18 = 45 kmph 10 5

1. A person standing on a railway platform noticed that a train took 21 seconds to completely pass through the platform which was 84 m long and it took 9 seconds in passing him. The speed of the train was
1. 25.2 km/hour
2. 32.4 km/hour
3. 50.4 km/hour
4. 75.6 km/hour

1. Let the length of train be x metres.
When the train crosses the standing man,

 its speed = x 9

When the train crosses the platform of length 84 m, its speed
 = x + 84 21

 Obviously, x = x + 84 9 21

⇒  21x – 9x = 9 × 84
⇒  12x = 9 × 84
 ⇒  x = 9 × 84 = 63 m 12

 ∴   Required speed = 63 m/sec 9

 = 63 × 18 kmph = 25.2 kmph 9 5

##### Correct Option: A

Let the length of train be x metres.
When the train crosses the standing man,

 its speed = x 9

When the train crosses the platform of length 84 m, its speed
 = x + 84 21

 Obviously, x = x + 84 9 21

⇒  21x – 9x = 9 × 84
⇒  12x = 9 × 84
 ⇒  x = 9 × 84 = 63 m 12

 ∴   Required speed = 63 m/sec 9

 = 63 × 18 kmph = 25.2 kmph 9 5

1. A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train ?
1. 69.5 km/hr
2. 70 km/hr
3. 79 km/hr
4. 79.2 km/hr

1. Let the length of train be x metres.
Then, speed of train when it

 passes a telegraph post = x m/sec. 8

and speed of train, when it
 passes the bridge = x + 264 20

Clearly,
 x = x + 264 8 20

 ⇒ x = x + 264 2 5

⇒  5x = 2x + 528
⇒  3x = 528
 ⇒  x = 528 = 176m 3

 ∴   Speed of train = 176 = 22 m/sec. 8

 = 22 × 18 Kmph 5

= 79.2 kmph

##### Correct Option: D

Let the length of train be x metres.
Then, speed of train when it

 passes a telegraph post = x m/sec. 8

and speed of train, when it
 passes the bridge = x + 264 20

Clearly,
 x = x + 264 8 20

 ⇒ x = x + 264 2 5

⇒  5x = 2x + 528
⇒  3x = 528
 ⇒  x = 528 = 176m 3

 ∴   Speed of train = 176 = 22 m/sec. 8

 = 22 × 18 Kmph 5

= 79.2 kmph

1. A train passes a man standing on a platform in 8 seconds and also crosses the platform which is 264 metres long in 20 seconds. The length of the train (in metres) is :
1. 188
2. 176
3. 175
4. 96

1. Rule 10 and Rule 1,
Let length of train be x m

 ∴   Speed of train = x + 264 20

 Also, speed of train = x 8

 Obviously, x = x + 264 8 20

 ⇒ x = x + 264 2 5

⇒  5x = 2x + 528
⇒  5x – 2x = 528
⇒  x = 528 ÷ 3 = 176 m

##### Correct Option: B

Rule 10 and Rule 1,
Let length of train be x m

 ∴   Speed of train = x + 264 20

 Also, speed of train = x 8

 Obviously, x = x + 264 8 20

 ⇒ x = x + 264 2 5

⇒  5x = 2x + 528
⇒  5x – 2x = 528
⇒  x = 528 ÷ 3 = 176 m

1. A train passes a 50 metres long platform in 14 seconds and a man standing on the platform in 10 seconds.The speed of the train is :
1. 24 km/hr
2. 36 km/hr
3. 40 km/hr
4. 45 km/hr

1. Rule 10 and Rule 1,
Let the length of train be x metres
∴  According to question

 Speed of the train = x m/sec. 10

Also, the speed of the train
 = x + 50 m/sec. 14

[∵  It passes the platform in 14 seconds]
Both the speeds should be equal,
i.e.,
 x = x + 50 10 14

or 14x = 10x + 500
or 14x – 10x = 500
or 4x = 500
∴  x = 125 metres
 Hence, Speed = 125 = 12 5. m/sec. 10

 = 12.5 × 18 km/hr. 5

= 45 km/hr.

##### Correct Option: D

Rule 10 and Rule 1,
Let the length of train be x metres
∴  According to question

 Speed of the train = x m/sec. 10

Also, the speed of the train
 = x + 50 m/sec. 14

[∵  It passes the platform in 14 seconds]
Both the speeds should be equal,
i.e.,
 x = x + 50 10 14

or 14x = 10x + 500
or 14x – 10x = 500
or 4x = 500
∴  x = 125 metres
 Hence, Speed = 125 = 12 5. m/sec. 10

 = 12.5 × 18 km/hr. 5

= 45 km/hr.