## Speed, Time and Distance

#### Speed, Time and Distance

1. A man standing on a platform finds that a train takes 3 seconds to pass him and another train of the same length moving in the opposite direction, takes 4 seconds. The time taken by the trains to pass each other will be
1.  2 3 seconds 7
2.  3 3 seconds 7
3.  4 3 seconds 7
4.  5 3 seconds 7

1. Let the length of each train be x metres

 Then, Speed of first train = x m/sec 3

 Speed of second train = x m/sec 4

They are moving in opposite directions
 ∴ Required time = x + x 3 4

 = 4x + 3x = 7x m./sec. 12 12

Total length = x + x = 2 x m.
 ∴  Time taken = 2x 7x 12

 = 24 7

 = 3 3 sec. 7

##### Correct Option: B

Let the length of each train be x metres

 Then, Speed of first train = x m/sec 3

 Speed of second train = x m/sec 4

They are moving in opposite directions
 ∴ Required time = x + x 3 4

 = 4x + 3x = 7x m./sec. 12 12

Total length = x + x = 2 x m.
 ∴  Time taken = 2x 7x 12

 = 24 7

 = 3 3 sec. 7

1. Two trains 108 m and 112 m in length are running towards each other on the parallel lines at a speed of 45 km/hr and 54 km/ hr respectively. To cross each other after they meet, it will take
1. 12 sec
2. 9 sec
3. 8 sec
4. 10 sec

1. Relative speed = 45 + 54 = 99 kmph

 = 99 × 5 m/sec. 18

 or 55 m/sec. 2

 ∴   Required time = 108 + 112 55 2

 = 220 × 2 = 8 seconds 55

##### Correct Option: C

Relative speed = 45 + 54 = 99 kmph

 = 99 × 5 m/sec. 18

 or 55 m/sec. 2

 ∴   Required time = 108 + 112 55 2

 = 220 × 2 = 8 seconds 55

1. Two trains start from station A and B and travel towards each other at speed of 16 miles/ hour and 21 miles/ hour respectively. At the time of their meeting, the second train has travelled 60 miles more than the first. The distance between A and B (in miles) is :
1. 444
2. 496
3. 333
4. 540

1. Let the trains meet after t hours
Then, 21t – 16t = 60
⇒  5t = 60 ⇒ t = 12 hours
∴  Distance between A and B
= (16 + 21) × 12
= 37 × 12 = 444 miles
Second Method :
Here, a = 21, b = 16, d = 60

 Distance between A and B = a + b × d a − b

 = 21 + 16 × 60 21 − 16

 = 37 × 60 5

= 37 × 12 = 444 miles

##### Correct Option: A

Let the trains meet after t hours
Then, 21t – 16t = 60
⇒  5t = 60 ⇒ t = 12 hours
∴  Distance between A and B
= (16 + 21) × 12
= 37 × 12 = 444 miles
Second Method :
Here, a = 21, b = 16, d = 60

 Distance between A and B = a + b × d a − b

 = 21 + 16 × 60 21 − 16

 = 37 × 60 5

= 37 × 12 = 444 miles

1. Two trains 150 m and 120 m long respectively moving from opposite directions cross each other in 10 secs. If the speed of the second train is 43.2 km/hr, then the speed of the first train is
1. 54 km/hr
2. 50 km/hr
3. 52 km/hr
4. 51 km/hr

1. Speed of second train
= 43.2 kmph

 = 43.2 × 5 m/sec. 18

or 12 m/sec.Let the speed of first train be x m per second, then
 150 + 120 = 10 x + 12

⇒  27 = + x 12
⇒  x = 15 m/s
 = 15 × 18 kmph = 54 kmph 5

##### Correct Option: A

Speed of second train
= 43.2 kmph

 = 43.2 × 5 m/sec. 18

or 12 m/sec.Let the speed of first train be x m per second, then
 150 + 120 = 10 x + 12

⇒  27 = + x 12
⇒  x = 15 m/s
 = 15 × 18 kmph = 54 kmph 5

1. Two trains of length 137 metre and 163 metre are running with speed of 42 km/hr and 48 km/hr respectively towards each other on papallel tracks. In how many seconds will they cross each other?
1. 30 sec
2. 24 sec
3. 12 sec
4. 10 sec

1. Relative speed = 42 + 48 = 90 kmph

 = 90 × 5 m/s = 25 m/s 18

Sum of the length of both trains
= 137 + 163 = 300 metres
 ∴  Required time = 300 = 12 seconds. 25

##### Correct Option: C

Relative speed = 42 + 48 = 90 kmph

 = 90 × 5 m/s = 25 m/s 18

Sum of the length of both trains
= 137 + 163 = 300 metres
 ∴  Required time = 300 = 12 seconds. 25