## Speed, Time and Distance

#### Speed, Time and Distance

1. The time taken by a train 160 m long, running at 72 km/hr, in crossing an electric pole is
1. 8 seconds
2. 9 seconds
3. 6 seconds
4. 4 seconds

1. Distance covered in crossing a pole = Length of train
Speed of train = 72 kmph

 = 72 × 5 m./sec. 18

= 20 m./sec.
 ∴  Required time = 160 20

= 8 seconds

##### Correct Option: A

Distance covered in crossing a pole = Length of train
Speed of train = 72 kmph

 = 72 × 5 m./sec. 18

= 20 m./sec.
 ∴  Required time = 160 20

= 8 seconds

1. A train 150m long passes a km stone in 30 seconds and another train of the same length travelling in opposite direction in 10 seconds. The speed ot the second train is :
1. 90 km/hr
2. 125 km/hr
3. 25 km/hr
4. 75 km/hr

1.  ∴  Speed of train = 150 = 5 m/sec. 30

Speed of train B = x m/sec.
Relative speed = (5+x) m/sec.
∴  Length of both trains = Relative speed × Time
⇒  300 = (5 + x) × 10
 ⇒  5 + x = 300 = 30 10

⇒  x = 30 – 5 = 25 m/sec.
 = 25 × 18 kmph. 5

= 90 kmph.

##### Correct Option: A

 ∴  Speed of train = 150 = 5 m/sec. 30

Speed of train B = x m/sec.
Relative speed = (5+x) m/sec.
∴  Length of both trains = Relative speed × Time
⇒  300 = (5 + x) × 10
 ⇒  5 + x = 300 = 30 10

⇒  x = 30 – 5 = 25 m/sec.
 = 25 × 18 kmph. 5

= 90 kmph.

1. A train is 250m long. If the train takes 50 seconds to cross a tree by the railway line, then the speed of the train in km/hr is :
1. 10
2. 9
3. 5
4. 18

1.  Speed of train = Length of train Time taken in crossing

 = 250 = 5 m/sec. 50

 = 5 × 18 kmph. 5

= 18 kmph

##### Correct Option: D

 Speed of train = Length of train Time taken in crossing

 = 250 = 5 m/sec. 50

 = 5 × 18 kmph. 5

= 18 kmph

1. A train passes an electrical pole in 20 seconds and passes a platform 250 m long in 45 seconds. Find the length of the train.
1. 400m
2. 200m
3. 300m
4. 250m

1. If the length of train be x metre,
then speed of train

 = x = x + 250 20 45

 ⇒ x = x + 250 4 9

⇒  9x = 4x + 1000
⇒  9x – 4x = 1000
⇒  5x = 1000
 ⇒  x = 1000 = 200 metre 5

##### Correct Option: B

If the length of train be x metre,
then speed of train

 = x = x + 250 20 45

 ⇒ x = x + 250 4 9

⇒  9x = 4x + 1000
⇒  9x – 4x = 1000
⇒  5x = 1000
 ⇒  x = 1000 = 200 metre 5

1. If a man walks at the rate of 5 km/hour, he misses a train by 7 minutes. However if he walks at the rate of 6 km/hour, he reaches the station 5 minutes before the arrival of the train. The distance covered by him to reach the station is
1. 6 km
2. 7 km
3. 6.25 km
4. 4 km

1. Let the required distance be x km.
Difference of time = 7 + 5 = 12

 minutes = 1 hour 5

 Time = Distance Speed

According to the question,
 x − x = 1 5 6 5

 ⇒ 6x − 5x = 1 30 5

 ⇒ x = 1 30 5

 ⇒  x = 30 = 6 km. 5

##### Correct Option: D

Let the required distance be x km.
Difference of time = 7 + 5 = 12

 minutes = 1 hour 5

 Time = Distance Speed

According to the question,
 x − x = 1 5 6 5

 ⇒ 6x − 5x = 1 30 5

 ⇒ x = 1 30 5

 ⇒  x = 30 = 6 km. 5