Speed, Time and Distance
- A man travels some distance at a speed of 12 km/hr and returns at a speed of 9 km/hr. If the total time taken by him is 2 hrs 20 minutes the distance is
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Let the required distance be x km.
Time = 2 hours 20 minutes 2 1 hours 3
According to the question,x + x = 7 12 9 3 ⇒ 3x + 4x = 7 36 3 ⇒ 7x = 7 36 3 ⇒ x = 7 × 36 = 12 km. 3 7 Correct Option: D
Let the required distance be x km.
Time = 2 hours 20 minutes 2 1 hours 3
According to the question,x + x = 7 12 9 3 ⇒ 3x + 4x = 7 36 3 ⇒ 7x = 7 36 3 ⇒ x = 7 × 36 = 12 km. 3 7
- The length of a train and that of a platform are equal. If with a speed of 90 km/hr the train
crosses the platform in one minute, then the length of the train (in metres) is :
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Let the length of train be x metre
Speed = 90 km/hr= 90 × 5 metre/sec. 18
= 25 metre/sec.
∴ Distance covered in 60 sec.
= 25 × 60 = 1500 metres
Now, according to question,
2x = 1500
∴ x = 750 metreCorrect Option: C
Let the length of train be x metre
Speed = 90 km/hr= 90 × 5 metre/sec. 18
= 25 metre/sec.
∴ Distance covered in 60 sec.
= 25 × 60 = 1500 metres
Now, according to question,
2x = 1500
∴ x = 750 metre
- A train passes two bridges of lengths 800 m and 400 m in 100 seconds and 60 seconds
respectively. The length of the train is :
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When a train crosses a bridge it covers the distance equal to length of Bridge & its own length
Let the length of the train be = x∴ Speed of the train = x + 800 m/s 100
Since train passes the 800 m bridge in 100 seconds.
Again, train passes the 400 m bridge in 60 seconds.∴ 400 + x = 60 x + 800 100 ⇒ (400 + x) × 100 = 60 x + 800
⇒ 40000 + 100x
= 60x + 48000
⇒ 100x – 60x = 48000 – 40000
⇒ 40x = 8000∴ x = 8000 = 200m 40 Correct Option: C
When a train crosses a bridge it covers the distance equal to length of Bridge & its own length
Let the length of the train be = x∴ Speed of the train = x + 800 m/s 100
Since train passes the 800 m bridge in 100 seconds.
Again, train passes the 400 m bridge in 60 seconds.∴ 400 + x = 60 x + 800 100 ⇒ (400 + x) × 100 = 60 x + 800
⇒ 40000 + 100x
= 60x + 48000
⇒ 100x – 60x = 48000 – 40000
⇒ 40x = 8000∴ x = 8000 = 200m 40
- A train 300 metres long is running at a speed of 25 metres per second. It will cross a bridge of 200 metres in
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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/sect = x + y u = 300 + 200 25 = 500 25
t = 20 secondsCorrect 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/sect = x + y u = 300 + 200 25 = 500 25
t = 20 seconds
- 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 :
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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 = ?
usingt = x + y u 60 = 800 + y 65 3 60 × 65 = 800 + y 3
1300 – 800 = y
y = 500 metresCorrect 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 = ?
usingt = x + y u 60 = 800 + y 65 3 60 × 65 = 800 + y 3
1300 – 800 = y
y = 500 metres
