## Speed, Time and Distance

#### Speed, Time and Distance

1. Two trains of equal length, running in opposite directions, pass a pole in 18 and 12 seconds. The trains will cross each other in
1. 14.4 seconds
2. 15.5 seconds
3. 18.8 seconds
4. 20.2 seconds

1. Let the length of each train be x metre.

 Speed of first train = x m/sec 18

 Speed of second train = x m/sec 12

When both trains cross each other, time taken
 = 2x x + x 18 12

 = 2x 2x + 3x 36

 = 2x × 36 5x

 = 72 = 14.4 seconds 5

##### Correct Option: A

Let the length of each train be x metre.

 Speed of first train = x m/sec 18

 Speed of second train = x m/sec 12

When both trains cross each other, time taken
 = 2x x + x 18 12

 = 2x 2x + 3x 36

 = 2x × 36 5x

 = 72 = 14.4 seconds 5

1. Two trains 105 metres and 90 metres long, runs at the speed of 45 km/hr and 72 km/hr respectively, in opposite directions on parallel tracks. The time which they take to cross each other, is
1. 8 seconds
2. 6 seconds
3. 7 seconds
4. 5 seconds

1. Length of both trains
= 105 + 90 = 195 m.
Relative speed = (45 + 72) = 117 kmph

 = 117 × 5 or 65 m/sec. 18 2

 ∴  Time taken = 195 65 2

 = 195 × 2 = 6 seconds 65

##### Correct Option: B

Length of both trains
= 105 + 90 = 195 m.
Relative speed = (45 + 72) = 117 kmph

 = 117 × 5 or 65 m/sec. 18 2

 ∴  Time taken = 195 65 2

 = 195 × 2 = 6 seconds 65

1. Two trains are moving on two parallel tracks but in opposite directions. A person sitting in the train moving at the speed of 80 km/hr passes the second train in 18 seconds. If the length of the second train is 1000 m, its speed is
1. 100 km/hr
2. 120 km/hr
3. 140 km/hr
4. 150 km/hr

1. Let the speed of second train be x m/s.

 80 km/h = 80 × 5 m/s 18

According to the question
 1000 = 18 x + 80 × 5 18

⇒  1000 = 18x + 400
 ∴  x = 600 m/s 18

 = 600 × 18 km/h = 120 km/h 18 5

##### Correct Option: B

Let the speed of second train be x m/s.

 80 km/h = 80 × 5 m/s 18

According to the question
 1000 = 18 x + 80 × 5 18

⇒  1000 = 18x + 400
 ∴  x = 600 m/s 18

 = 600 × 18 km/h = 120 km/h 18 5

1. Two trains start from stations A and B and travel towards each other at speed of 50 km/hour and 60 km/hour respectively. At the time of their meeting, the second train has travelled 120 km more than the first. The distance between A and B is :
1. 990 km
2. 1200 km
3. 1320 km
4. 1440 km

1. Let train A start from station A and B from station B.
Let the trains A and B meet after t hours.
∴  Distance covered by train A in t hours = 50t
Distance covered by train B in t hours = 60t km
According to the question,
60t – 50t = 120

 ⇒  t = 120 = 12 hours. 10

∴  Distance AB = 50 × 12 + 60 ×
12 = 600 + 720 = 1320 km
Second Method :
Here, a = 60, b = 50, d = 120
 Distance between A and B = a + b × d a − b

 = 60 + 50 × 120 60 − 50

 = 110 × 120 = 1320 km 10

##### Correct Option: C

Let train A start from station A and B from station B.
Let the trains A and B meet after t hours.
∴  Distance covered by train A in t hours = 50t
Distance covered by train B in t hours = 60t km
According to the question,
60t – 50t = 120

 ⇒  t = 120 = 12 hours. 10

∴  Distance AB = 50 × 12 + 60 ×
12 = 600 + 720 = 1320 km
Second Method :
Here, a = 60, b = 50, d = 120
 Distance between A and B = a + b × d a − b

 = 60 + 50 × 120 60 − 50

 = 110 × 120 = 1320 km 10

1. Two trains 140 m and 160 m long run at the speed of 60 km/ hour and 40 km/hour respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is :
1. 10 sec.
2. 10.8 sec.
3. 9 sec.
4. 9.6 sec.

1. Total length of trains
= 140 + 160 = 300 m.
Relative speed = 60 + 40 = 100 kmph

 = 100 × 5 m/sec. 18

 or 250 m/sec. 9

∴  Time taken to cross each other
 = 300 250 9

 = 300 × 9 = 10.8 sec. 250

##### Correct Option: B

Total length of trains
= 140 + 160 = 300 m.
Relative speed = 60 + 40 = 100 kmph

 = 100 × 5 m/sec. 18

 or 250 m/sec. 9

∴  Time taken to cross each other
 = 300 250 9

 = 300 × 9 = 10.8 sec. 250