## Speed, Time and Distance

#### Speed, Time and Distance

1. Two trains 125 metres and 115 metres in length, are running towards each other on parallel lines, one at the rate of 33 km/hr and the other at 39 km/hr. How much time (in seconds) will they take to pass each other from the moment they meet ?
1. 8
2. 10
3. 12
4. 15

1. Relative speed
= (33 + 39) kmph
= 72 kmph

 = 72 × 5 m/sec. 18

= 20 m/sec.
 ∴   Time taken in crossing = Length of both trains Relative speed

 = 125 + 115 = 240 20 20

= 12 seconds

##### Correct Option: C

Relative speed
= (33 + 39) kmph
= 72 kmph

 = 72 × 5 m/sec. 18

= 20 m/sec.
 ∴   Time taken in crossing = Length of both trains Relative speed

 = 125 + 115 = 240 20 20

= 12 seconds

1. A goods train starts running from a place at 1 P.M. at the rate of 18 km/hour. Another goods train starts from the same place at 3 P.M. in the same direction and overtakes the first train at 9 P.M. The speed of the second train in km/hr is
1. 24
2. 30
3. 15
4. 18

1. Distance covered by the first goods train in 8 hours = Distance covered by the second goods train in 6 hours.
⇒  18 × 8 = 6 × x

 ⇒  x = 18 × 8 = 24 kmph 6

##### Correct Option: A

Distance covered by the first goods train in 8 hours = Distance covered by the second goods train in 6 hours.
⇒  18 × 8 = 6 × x

 ⇒  x = 18 × 8 = 24 kmph 6

1. Two trains, 80 metres and 120 metres long, are running at the speed of 25 km/hr and 35 km/hr respectively in the same direction on parallel tracks. How many seconds will they take to pass each other ?
1. 48
2. 64
3. 70
4. 72

1. Relative speed = 35 – 25 = 10 kmph

 = 10 × 5 m/sec. 18

Total length = 80 + 120 = 200 metres
 ∴   Required time = Sum of the lengths of trains Relative speed

 = 200 10 × 5 18

 = 200 × 18 = 72 seconds 10 × 5

##### Correct Option: D

Relative speed = 35 – 25 = 10 kmph

 = 10 × 5 m/sec. 18

Total length = 80 + 120 = 200 metres
 ∴   Required time = Sum of the lengths of trains Relative speed

 = 200 10 × 5 18

 = 200 × 18 = 72 seconds 10 × 5

1. Two trains, of same length, are running on parallel tracks in the same direction with speed 60 km/hour and 90 km/hour respectively. The latter completely crosses the former in 30 seconds. The length of each train (in metres) is
1. 125
2. 150
3. 100
4. 115

1. When two trains cross each other, they cover distance equal to the sum of their length with relative speed.
Let length of each train = x metre
Relative speed = 90 – 60
= 30 kmph

 = 30 × 5 m/sec. 18

 = 25 m/sec. 3

 ∴ 2x = 30 25 3

 ⇒  2x = 30 × 25 3

⇒  2x = 250
⇒  x = 125 metres

##### Correct Option: A

When two trains cross each other, they cover distance equal to the sum of their length with relative speed.
Let length of each train = x metre
Relative speed = 90 – 60
= 30 kmph

 = 30 × 5 m/sec. 18

 = 25 m/sec. 3

 ∴ 2x = 30 25 3

 ⇒  2x = 30 × 25 3

⇒  2x = 250
⇒  x = 125 metres

1. Two trains 180 metres and 120 metres in length are running towards each other on parallel tracks, one at the rate 65 km/hour and another at 55 km/hour. In how many seconds will they be clear of each other from the moment they meet ?
1. 6
2. 9
3. 12
4. 15

1.  Required time = Sum of the lengths of trains Relative speed

Relative speed = 65 + 55
= 120 kmph
 Required time = 180 + 120 120 × 5 18

 = 300 × 18 = 9 seconds 120 × 5

##### Correct Option: B

 Required time = Sum of the lengths of trains Relative speed

Relative speed = 65 + 55
= 120 kmph
 Required time = 180 + 120 120 × 5 18

 = 300 × 18 = 9 seconds 120 × 5