## Speed, Time and Distance

#### Speed, Time and Distance

1. A train travelling with uniform speed crosses two bridges of lengths 300 m and 240 m in 21
seconds and 18 seconds respectively. The speed of the train is :
1. 72 km/hr
2. 68 km/hr
3. 65 km/hr
4. 60 km/hr

1. Let the length of the train be x.

 ∴  Speed of the train = x + 300 = x + 240 21 18

 ⇒ x + 300 = x + 240 7 6

⇒  7x + 1680 = 6x + 1800
⇒  x = 120
 ∴  Speed of the train = x + 300 = 420 = 20 m/sec 21 21

 = 20 × 18 kmph = 72 kmph 5

##### Correct Option: A

Let the length of the train be x.

 ∴  Speed of the train = x + 300 = x + 240 21 18

 ⇒ x + 300 = x + 240 7 6

⇒  7x + 1680 = 6x + 1800
⇒  x = 120
 ∴  Speed of the train = x + 300 = 420 = 20 m/sec 21 21

 = 20 × 18 kmph = 72 kmph 5

1. A train, with a uniform speed, crosses a platform, 162 metres long, in 18 seconds and another platform, 120 metres long, in 15 seconds. The speed of the train is
1. 14 km/hr
2. 42 km/hr
3. 50.4 km/hr
4. 67.2 km/hr

1. Let the Length of the train be x

 Then, x + 162 = x + 120 18 15

(Speed of the train)
 ⇒ x + 162 = x + 120 6 5

⇒  6x + 720 = 5x + 810
⇒  x = 810 – 720 = 90
 ∴  Speed of the train = 90 + 162 m/sec. 18

 = 252 × 18 kmph 18 5

= 50.4 kmph

##### Correct Option: C

Let the Length of the train be x

 Then, x + 162 = x + 120 18 15

(Speed of the train)
 ⇒ x + 162 = x + 120 6 5

⇒  6x + 720 = 5x + 810
⇒  x = 810 – 720 = 90
 ∴  Speed of the train = 90 + 162 m/sec. 18

 = 252 × 18 kmph 18 5

= 50.4 kmph

1. A train with a uniform speed passes a platform, 122 metres long, in 17 seconds and a bridge, 210 metres long, in 25 seconds. The speed of the train is
1. 46.5 km/hour
2. 37.5 km/hour
3. 37.6 km/hour
4. 39.6 km/hour

1. Let the length of the train be x
According to the question,

 x + 122 = x + 210 17 25

⇒  25x + 3050 = 17x + 3570
⇒  25x – 17x = 3570 – 3050
⇒  8x = 520
 ⇒  x = 520 = 65 metres 8

 ∴  Speed of the train = 65 + 122 17

 = 187 metre/second 17

= 11 metre/second
 = 11 × 18 kmph 5

= 39.6 kmph

##### Correct Option: D

Let the length of the train be x
According to the question,

 x + 122 = x + 210 17 25

⇒  25x + 3050 = 17x + 3570
⇒  25x – 17x = 3570 – 3050
⇒  8x = 520
 ⇒  x = 520 = 65 metres 8

 ∴  Speed of the train = 65 + 122 17

 = 187 metre/second 17

= 11 metre/second
 = 11 × 18 kmph 5

= 39.6 kmph

1. A train travelling at a speed of 30 m/sec crosses a platform, 600 metres long, in 30 seconds. The length (in metres) of train is
1. 120
2. 150
3. 200
4. 300

1. Let the length of train be x
According to the question,

 x + 600 = 30 30

⇒  x + 600 = 900
⇒  x = 900 – 600 = 300 m

##### Correct Option: D

Let the length of train be x
According to the question,

 x + 600 = 30 30

⇒  x + 600 = 900
⇒  x = 900 – 600 = 300 m

1. A 120 metre long train is running at a speed of 90 km per hour. It will cross a railway platform 230 m long in :
1.  4 4 seconds 5
2.  9 1 seconds 5
3. 7 seconds
4. 14 seconds

1. Speed of train = 90 kmph

 = 90 × 5 = 25 m/sec 18

Distance covered
= 230 + 120 = 350 m
 ∴  Time taken = 350 = 14 seconds 25

##### Correct Option: D

Speed of train = 90 kmph

 = 90 × 5 = 25 m/sec 18

Distance covered
= 230 + 120 = 350 m
 ∴  Time taken = 350 = 14 seconds 25