## Speed, Time and Distance

#### Speed, Time and Distance

1. A train leaves a station A at 7 am and reaches another station B at 11 am. Another train leaves B at 8 am and reaches A at 11.30 am. The two trains cross one another at
1. 8:36 am
2. 8:56 am
3. 9:00 am
4. 9:24 am

1. Let both trains meet after t hours since 7 a.m.
Distance between stations A and B = x Km.

 ∴ x × t + x × (t − 1) = x 4 7/2 Speed = Distance Time

 ⇒ t + 2(t − 1) = 1 4 7

 ⇒ 7t + 8t − 8 = 1 28

⇒  15 t – 8 = 28
⇒  15 t = 28 + 8 = 36
 ⇒   t = 36 = 12 hours 15 5

= 2 hours 24 minutes
∴  Required time = 9 :24 a.m.

##### Correct Option: D

Let both trains meet after t hours since 7 a.m.
Distance between stations A and B = x Km.

 ∴ x × t + x × (t − 1) = x 4 7/2 Speed = Distance Time

 ⇒ t + 2(t − 1) = 1 4 7

 ⇒ 7t + 8t − 8 = 1 28

⇒  15 t – 8 = 28
⇒  15 t = 28 + 8 = 36
 ⇒   t = 36 = 12 hours 15 5

= 2 hours 24 minutes
∴  Required time = 9 :24 a.m.

1. A train crosses a platform in 30 seconds travelling with a speed of 60 km/h. If the length of the train be 200 metres, then the length (in metres) of the platform is
1. 400
2. 300
3. 200
4. 500

1. Speed of train = 60 kmph

 = 60 × 5 m/sec. 18

 = 50 m/sec. 3

If the length of platform be = x metre, then
 ∴  Speed of train = Length of (train + platform) Time taken in crossing

 ⇒ 50 = 200 + x 3 30

⇒  50 × 10 = 200 + x
⇒  x = 500 – 200 = 300 metre

##### Correct Option: B

Speed of train = 60 kmph

 = 60 × 5 m/sec. 18

 = 50 m/sec. 3

If the length of platform be = x metre, then
 ∴  Speed of train = Length of (train + platform) Time taken in crossing

 ⇒ 50 = 200 + x 3 30

⇒  50 × 10 = 200 + x
⇒  x = 500 – 200 = 300 metre

1. A train moving at a rate of 36 km/hr. crosses a standing man in 10 seconds. It will cross a platform 55 metres long, in :
1. 6 seconds
2. 7 seconds
3.  15 1 seconds 2
4.  5 1 seconds 2

1. Speed of train = 36 kmph

 = 36 × 5 = 10 m/sec 18

Length of train = 10 × 10 = 100 metres
 ∴  Required time = 100 + 55 10

 = 15 5 = 15 1 second 10 2

= 15.5 seconds

##### Correct Option: C

Speed of train = 36 kmph

 = 36 × 5 = 10 m/sec 18

Length of train = 10 × 10 = 100 metres
 ∴  Required time = 100 + 55 10

 = 15 5 = 15 1 second 10 2

= 15.5 seconds

1. A train passes by a lamp post on a platform in 7 sec. and passes by the platform completely in 28 sec. If the length of the platform is 390 m, then length of the train (in metres) is
1. 120
2. 130
3. 140
4. 150

1. Let the length of train be x metre, then

 ∴  Speed of train = x = x + 390 7 28

 ⇒  x = x + 390 4

⇒  4x – x = 390
 ⇒  x = 390 = 130 metres 3

##### Correct Option: B

Let the length of train be x metre, then

 ∴  Speed of train = x = x + 390 7 28

 ⇒  x = x + 390 4

⇒  4x – x = 390
 ⇒  x = 390 = 130 metres 3

1. Two trains 100 metres and 95 metres long respectively pass each other in 27 seconds when they run in the same direction and in 9 seconds when they run in opposite directions. Speed of the two trains are
1. 44 km/hr, 22 km/hr
2. 52 km/hr, 26 km/hr
3. 36 km/hr. 18 km/hr
4. 40 km/hr, 20 km/hr

1. Let the speed of trains be x and y metre/sec respectively,

 100 + 95 = 27 x − y

 ⇒  x − y = 195 = 65 .....(i) 27 9

Again,
 195 = 9 x + y

 ⇒  x + y = 195 .....(ii) 9

By equation (i) + (ii)
 ⇒  2x = 65 + 195 = 260 9 9 9

 ⇒  x = 260 = 130 m/sec. 2 × 9 9

 = 130 × 18 kmph = 52 kmph 9 5

From equation (ii),
 y = 195 − 130 = 65 m/sec. 9 9 9

 = 65 × 18 = 26 kmph 9 5

##### Correct Option: B

Let the speed of trains be x and y metre/sec respectively,

 100 + 95 = 27 x − y

 ⇒  x − y = 195 = 65 .....(i) 27 9

Again,
 195 = 9 x + y

 ⇒  x + y = 195 .....(ii) 9

By equation (i) + (ii)
 ⇒  2x = 65 + 195 = 260 9 9 9

 ⇒  x = 260 = 130 m/sec. 2 × 9 9

 = 130 × 18 kmph = 52 kmph 9 5

From equation (ii),
 y = 195 − 130 = 65 m/sec. 9 9 9

 = 65 × 18 = 26 kmph 9 5