## Speed, Time and Distance

#### Speed, Time and Distance

1. A train, 150 m long, takes 30 seconds to cross a bridge 500 m long. How much time will the train take to cross a platform 370 m long ?
1. 36 secs
2. 30 secs
3. 24 secs
4. 18 secs

1. When a train croses a bridge, distance covered = length of (bridge + train).

 ∴  Speed of train = 150 + 500 30

 = 650 = 65 m/sec. 30 3

∴ Time taken to cross the 370m long platform
 = 370 + 150 65 3

 = 520 × 3 = 24 seconds 65

##### Correct Option: C

When a train croses a bridge, distance covered = length of (bridge + train).

 ∴  Speed of train = 150 + 500 30

 = 650 = 65 m/sec. 30 3

∴ Time taken to cross the 370m long platform
 = 370 + 150 65 3

 = 520 × 3 = 24 seconds 65

1. A train takes 18 seconds to pass through a platform 162 m long and 15 seconds to pass through another platform 120 m long. The length of the train (in m) is :
1. 70
2. 80
3. 90
4. 105

1. Let the length of the train be x metres.
When a train corsses a platform it covers a distance equal to the sum of lengths of train and platform. Also, the speed of train is same.

 ∴ x + 162 = x + 120 18 15

⇒  6x + 720 = 5x + 810
⇒  6x – 5x = 810 – 720
⇒  x = 90
∴  The length of the train = 90m.

##### Correct Option: C

Let the length of the train be x metres.
When a train corsses a platform it covers a distance equal to the sum of lengths of train and platform. Also, the speed of train is same.

 ∴ x + 162 = x + 120 18 15

⇒  6x + 720 = 5x + 810
⇒  6x – 5x = 810 – 720
⇒  x = 90
∴  The length of the train = 90m.

1. A train is moving at a speed of 132 km/hour. If the length of the train is 110 metres, how long will it take to cross a railway platform 165 metres long?
1. 5 seconds
2. 7.5 seconds
3. 10 seconds
4. 15 seconds

1. When a train crosses a railway platform, it travels a distance equal to sum of length of platform and its own length.
Speed = 132 kmph

 = 132 × 5 = 110 m/sec 18 3

∴  Required time

 = 110 + 165 seconds 110 3

 = 275 × 3 = 7.5 seconds 110

Second Method :
Here, x = 110m,
u = 132 km/hr.
 = 132 × 5 = 110 m/sec 18 3

y = 165m, t = ?
using
 t = x + y u

 t = 110 + 165 110 3

 t = 275 × 3 110

 = 25 × 3 = 15 = 7.5 sec 10 2

##### Correct Option: B

When a train crosses a railway platform, it travels a distance equal to sum of length of platform and its own length.
Speed = 132 kmph

 = 132 × 5 = 110 m/sec 18 3

∴  Required time

 = 110 + 165 seconds 110 3

 = 275 × 3 = 7.5 seconds 110

Second Method :
Here, x = 110m,
u = 132 km/hr.
 = 132 × 5 = 110 m/sec 18 3

y = 165m, t = ?
using
 t = x + y u

 t = 110 + 165 110 3

 t = 275 × 3 110

 = 25 × 3 = 15 = 7.5 sec 10 2

1. A train 800 metres long is running at the speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in metres) is :
1. 77200
2. 500
3. 1300
4. 13

1. When a train crosses a tunnel, it covers a distance equal to the sum of its own length and
tunnel.
Let the length of tunnel be x
Speed = 78 kmph

 = 78 × 1000 m/sec. = 65 m/sec. 60 × 60 3

 ∴  Speed = Distance Time

 ⇒ 65 = 800 + x 3 60

⇒  (800 + x ) × 3 = 65× 60
⇒  800 + x = 65 × 20 m
⇒  x = 1300 – 800 = 500
∴  Length of tunnel = 500 metres.

Second Method :
Here, x = 800 m,
u = 78 km/hr
 = 78 5 = 65 m/sec 18 3

t = 1 min = 60 sec, y = ?
using
 t = x + y u

 60 = 800 + y 65 3

 60 × 65 = 800 + y 3

1300 – 800 = y
y = 500 metres

##### Correct Option: B

When a train crosses a tunnel, it covers a distance equal to the sum of its own length and
tunnel.
Let the length of tunnel be x
Speed = 78 kmph

 = 78 × 1000 m/sec. = 65 m/sec. 60 × 60 3

 ∴  Speed = Distance Time

 ⇒ 65 = 800 + x 3 60

⇒  (800 + x ) × 3 = 65× 60
⇒  800 + x = 65 × 20 m
⇒  x = 1300 – 800 = 500
∴  Length of tunnel = 500 metres.

Second Method :
Here, x = 800 m,
u = 78 km/hr
 = 78 5 = 65 m/sec 18 3

t = 1 min = 60 sec, y = ?
using
 t = x + y u

 60 = 800 + y 65 3

 60 × 65 = 800 + y 3

1300 – 800 = y
y = 500 metres

1. A train 300 metres long is running at a speed of 25 metres per second. It will cross a bridge of 200 metres in
1. 5 seconds
2. 10 seconds
3. 20 seconds
4. 25 seconds

1. In crossing the bridge, the train travels its own length plus the length of the bridge.
Total distance (length)
= 300 + 200 = 500 m.
Speed = 25m/sec.
∴  The required time
= 500 ÷ 25 = 20 seconds
Second Method :
Here, x = 300m, y= 200 m, t = ?
u= 25 m/sec

 t = x + y u

 = 300 + 200 25

 = 500 25

t = 20 seconds

##### Correct Option: C

In crossing the bridge, the train travels its own length plus the length of the bridge.
Total distance (length)
= 300 + 200 = 500 m.
Speed = 25m/sec.
∴  The required time
= 500 ÷ 25 = 20 seconds
Second Method :
Here, x = 300m, y= 200 m, t = ?
u= 25 m/sec

 t = x + y u

 = 300 + 200 25

 = 500 25

t = 20 seconds