## Speed, Time and Distance

#### Speed, Time and Distance

1. Two trains of equal length take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction ?
1. 16
2. 15
3. 12
4. 10

1. When a train crosses a telegraph post, it covers its own length.

 ∴  Speed of first train = 120 = 12 m/sec. 10

 Speed of second train = 120 = 8 m/sec. 15

Relative speed = 12 + 8 = 20 m/sec.
 Required time = Total length of trains Relative Speed

 = 2 × 120 = 12 seconds. 20

##### Correct Option: C

When a train crosses a telegraph post, it covers its own length.

 ∴  Speed of first train = 120 = 12 m/sec. 10

 Speed of second train = 120 = 8 m/sec. 15

Relative speed = 12 + 8 = 20 m/sec.
 Required time = Total length of trains Relative Speed

 = 2 × 120 = 12 seconds. 20

1. Two trains of length 70 m and 80 m are running at speed of 68 km/hr and 40 km/hr respectively on parallel tracks in opposite directions. In how many seconds will they pass each other ?
1. 10 sec
2. 8 sec
3. 5 sec
4. 3 sec

1. Relative speed
= (68 + 40) kmph = 108 kmph

 = 108 × 5 m/s or 30 m/s 18

 ∴  Required time = Sum of the lengths of both trains Relative Speed

 = 70 + 80 second = 5 seconds 30

##### Correct Option: C

Relative speed
= (68 + 40) kmph = 108 kmph

 = 108 × 5 m/s or 30 m/s 18

 ∴  Required time = Sum of the lengths of both trains Relative Speed

 = 70 + 80 second = 5 seconds 30

1. Two towns A and B are 500 km. apart. A train starts at 8 AM from A towards B at a speed of 70 km/hr. At 10 AM, another train starts from B towards A at a speed of 110 km/hr. When will the two trains meet ?
1. 1 PM
2. 12 Noon
3. 12.30 PM
4. 1.30 PM

1. Let two trains meet after t hours when the train from town A leaves at 8 AM.
∴  Distance covered in t hours at 70 kmph + Distance covered in
(t – 2) hours at 110 kmph = 500km
∴  70t + 110 (t – 2) = 500
⇒  70t + 110t – 220 = 500
⇒  180 t = 500 + 220 = 720

 ⇒  t = 720 = 4 hours 180

Hence, the trains will meet at 12 noon.

##### Correct Option: B

Let two trains meet after t hours when the train from town A leaves at 8 AM.
∴  Distance covered in t hours at 70 kmph + Distance covered in
(t – 2) hours at 110 kmph = 500km
∴  70t + 110 (t – 2) = 500
⇒  70t + 110t – 220 = 500
⇒  180 t = 500 + 220 = 720

 ⇒  t = 720 = 4 hours 180

Hence, the trains will meet at 12 noon.

1. A train travelling at 48 km/hr crosses another train, having half its length and travelling in opposite direction at 42 km/hr, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the railway platform is
1. 200 m
2. 300 m
3. 350 m
4. 400 m

1. Let the length of the train travelling at 48 kmph be x metres.
Let the length of the platform be y metres.
Relative speed of train
= (48 + 42) kmph

 = 90 × 5 m./sec. 18

= 25 m./sec.
and 48 kmph
 = 48 × 5 = 40 m./sec. 18 3

According to the question,
 x + 1 = 2 25

= 12
 ⇒ 3x = 12 2 × 25

⇒  3x = 2 × 12 × 25 = 600
⇒  x = 200 m.
 Also, 200 + y = 45 40/3

⇒  600 + 3y = 40 × 45
⇒  3y = 1800 – 600 = 1200
 ⇒  y = 1200 = 400 m. 3

##### Correct Option: D

Let the length of the train travelling at 48 kmph be x metres.
Let the length of the platform be y metres.
Relative speed of train
= (48 + 42) kmph

 = 90 × 5 m./sec. 18

= 25 m./sec.
and 48 kmph
 = 48 × 5 = 40 m./sec. 18 3

According to the question,
 x + 1 = 2 25

= 12
 ⇒ 3x = 12 2 × 25

⇒  3x = 2 × 12 × 25 = 600
⇒  x = 200 m.
 Also, 200 + y = 45 40/3

⇒  600 + 3y = 40 × 45
⇒  3y = 1800 – 600 = 1200
 ⇒  y = 1200 = 400 m. 3

1. A train, 150m long, passes a pole in 15 seconds and another train of the same length travelling in the opposite direction in 12 seconds. The speed of the second train is
1. 45 km./hr
2. 48 km./hr
3. 52 km./hr
4. 54 km./hr

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

 Speed of first train = 150 = 10 m/sec 15

Relative speed of trains
= (x + 10) m/s
Total distance covered
= 150 + 150 = 300 metre
 ∴  Time taken = 300 x + 10

 ⇒ 300 = 12 x + 10

⇒  12x + 120 = 300
⇒  12x = 300 – 120 = 180
 ⇒  x = 180 = 15 m/s 12

 = 15 × 18 or 54 kmph. 5

##### Correct Option: D

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

 Speed of first train = 150 = 10 m/sec 15

Relative speed of trains
= (x + 10) m/s
Total distance covered
= 150 + 150 = 300 metre
 ∴  Time taken = 300 x + 10

 ⇒ 300 = 12 x + 10

⇒  12x + 120 = 300
⇒  12x = 300 – 120 = 180
 ⇒  x = 180 = 15 m/s 12

 = 15 × 18 or 54 kmph. 5