## Speed, Time and Distance

#### Speed, Time and Distance

1. A train is running at 36 km/hr. If it crosses a pole in 25 seconds, its length is
1. 248 m
2. 250 m
3. 255 m
4. 260 m

1. Speed of train = 36 kmph

 = 36 × 5 m/sec = 10 m/sec. 18

∴  Length of train
= Speed × time
= 10 × 25 = 250 metre

##### Correct Option: B

Speed of train = 36 kmph

 = 36 × 5 m/sec = 10 m/sec. 18

∴  Length of train
= Speed × time
= 10 × 25 = 250 metre

1. A train, 240 m long crosses a man walking along the line in opposite direction at the rate of 3 kmph in 10 seconds. The speed of the train is
1. 63 kmph
2. 75 kmph
3. 83.4 kmph
4. 86.4 kmph

1. If the speed of train be x kmph then,
Its relative speed = (x + 3) kmph

 ∴  Time = Length of the train Relative Speed

 ⇒ 10 3600

 240 = 1000 x + 3

 = 240 1000(x + 3)

⇒  x + 3 = 86.4
⇒  x = 83.4 kmph

##### Correct Option: C

If the speed of train be x kmph then,
Its relative speed = (x + 3) kmph

 ∴  Time = Length of the train Relative Speed

 ⇒ 10 3600

 240 = 1000 x + 3

 = 240 1000(x + 3)

⇒  x + 3 = 86.4
⇒  x = 83.4 kmph

1. A train, 300m long, passed a man, walking along the line in the same direction at the rate of 3 km/hr in 33 seconds. The speed of the train is
1. 30 km/h
2. 32 km/h
3.  32 8 km/h 11
4.  35 8 km/h 11

1. If the speed of the train be x kmph, then relative speed = (x – 3) kmph.

 or (x – 3) × 5 m/sec 18

 ∴ 300 = 33 (x − 3) × 5 18

⇒  5400 = 33 × 5 (x – 3)
⇒  360 = 11 (x – 3)
⇒  11x – 33 = 360
 ⇒  x = 393 = 35 8 kmph 11 11

##### Correct Option: D

If the speed of the train be x kmph, then relative speed = (x – 3) kmph.

 or (x – 3) × 5 m/sec 18

 ∴ 300 = 33 (x − 3) × 5 18

⇒  5400 = 33 × 5 (x – 3)
⇒  360 = 11 (x – 3)
⇒  11x – 33 = 360
 ⇒  x = 393 = 35 8 kmph 11 11

1. Buses start from a bus terminal with a speed of 20 km/hr at intervals of 10 minutes. What is the speed of a man coming from the opposite direction towards the bus terminal if he meets the buses at intervals of 8 minutes?
1. 3 km/hr
2. 4 km/hr
3. 5 km/hr
4. 7 km/hr

1. Distance covered in 10 minutes at 20kmph = distance covered in 8 minutes at (20 + x )
kmph

 ⇒  20 × 10 = 8 (20 + x ) 60 60

⇒  200 = 160 + 8x
⇒  8x = 40
 ⇒  x = 40 = 5 kmph 8

##### Correct Option: C

Distance covered in 10 minutes at 20kmph = distance covered in 8 minutes at (20 + x )
kmph

 ⇒  20 × 10 = 8 (20 + x ) 60 60

⇒  200 = 160 + 8x
⇒  8x = 40
 ⇒  x = 40 = 5 kmph 8

1. A passenger train 150m long is travelling with a speed of 36 km/ hr. If a man is cycling in the direction of train at 9 km/hr., the time taken by the train to pass the man is
1. 10 sec
2. 15 sec
3. 18 sec
4. 20 sec

1. Relative speed of train
= (36 – 9) kmph = 27 kmph

 = 27 × 5 m/sec 18

 = 15 m/sec 2

 ∴  Required time = Length of the train Relative speed

 = 150 × 2 = 20 seconds 15

##### Correct Option: D

Relative speed of train
= (36 – 9) kmph = 27 kmph

 = 27 × 5 m/sec 18

 = 15 m/sec 2

 ∴  Required time = Length of the train Relative speed

 = 150 × 2 = 20 seconds 15