Speed, Time and Distance
- In a one-kilometre race A, B and C are the three participants. A can give B a start of 50 m. and C a start of 69 m. The start, which B can allow C is
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Let the time taken to complete the race by A,B, and C be x minutes.
∴ Speed of A = 100 , x B = 1000 − 50 = 950 x x C = 1000 − 69 = 931 x x
Now, time taken to complete the race byB = 1000 = 1000 × x 950/x 950 and distance travelled by C in 1000x min 950 = 1000x × 931 = 980 km. 950 x
∴ B can allow C
= 1000 – 980 = 20 mCorrect Option: B
Let the time taken to complete the race by A,B, and C be x minutes.
∴ Speed of A = 100 , x B = 1000 − 50 = 950 x x C = 1000 − 69 = 931 x x
Now, time taken to complete the race byB = 1000 = 1000 × x 950/x 950 and distance travelled by C in 1000x min 950 = 1000x × 931 = 980 km. 950 x
∴ B can allow C
= 1000 – 980 = 20 m
- A train 110 metre long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?
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Relative speed of train
= (60 + 6) kmph.= 
66 × 5 
m/sec. 18 = 55 m/sec. 3
Length of train = 110 metre∴ Required time = 110 seconds 55/3 = 110 × 3 seconds 55
= 6 secondsCorrect Option: B
Relative speed of train
= (60 + 6) kmph.= 66 × 5 m/sec. 18 = 55 m/sec. 3
Length of train = 110 metre∴ Required time = 110 seconds 55/3 = 110 × 3 seconds 55
= 6 seconds
- The time for a train of length 110 metre running at the speed of 72 km/hr to cross a bridge of length 132 metre is
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Speed of train = 72 kmph.
= 72 × 5 m./sec. 18
= 20 m./sec.Required time = Length of train and bridge Speed of train = 110 + 132 seconds 20 = 242 seconds 20
= 12.1 secondsCorrect Option: B
Speed of train = 72 kmph.
= 72 × 5 m./sec. 18
= 20 m./sec.Required time = Length of train and bridge Speed of train = 110 + 132 seconds 20 = 242 seconds 20
= 12.1 seconds
- A train leaves a station A at 7 am and reaches another station B at 11 am. Another train leaves B at 8 am and reaches A at 11.30 am. The two trains cross one another at
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Let both trains meet after t hours since 7 a.m.
Distance between stations A and B = x Km.∴ x × t + x × (t − 1) = x 4 7/2 
Speed = Distance 
Time ⇒ t + 2(t − 1) = 1 4 7 ⇒ 7t + 8t − 8 = 1 28
⇒ 15 t – 8 = 28
⇒ 15 t = 28 + 8 = 36⇒ t = 36 = 12 hours 15 5
= 2 hours 24 minutes
∴ Required time = 9 :24 a.m.Correct Option: D
Let both trains meet after t hours since 7 a.m.
Distance between stations A and B = x Km.∴ x × t + x × (t − 1) = x 4 7/2 Speed = Distance Time ⇒ t + 2(t − 1) = 1 4 7 ⇒ 7t + 8t − 8 = 1 28
⇒ 15 t – 8 = 28
⇒ 15 t = 28 + 8 = 36⇒ t = 36 = 12 hours 15 5
= 2 hours 24 minutes
∴ Required time = 9 :24 a.m.
- A train crosses a platform in 30 seconds travelling with a speed of 60 km/h. If the length of the train be 200 metres, then the length (in metres) of the platform is
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Speed of train = 60 kmph
= 60 × 5 m/sec. 18 = 50 m/sec. 3
If the length of platform be = x metre, then∴ Speed of train = Length of (train + platform) Time taken in crossing ⇒ 50 = 200 + x 3 30
⇒ 50 × 10 = 200 + x
⇒ x = 500 – 200 = 300 metreCorrect Option: B
Speed of train = 60 kmph
= 60 × 5 m/sec. 18 = 50 m/sec. 3
If the length of platform be = x metre, then∴ Speed of train = Length of (train + platform) Time taken in crossing ⇒ 50 = 200 + x 3 30
⇒ 50 × 10 = 200 + x
⇒ x = 500 – 200 = 300 metre
