Speed, Time and Distance
- Two places P and Q are 162 km apart. A train leaves P for Q and simultaneously another train leaves Q for P. They meet at the end of 6 hours. If the former train travels 8 km/hour faster than the other, then speed of train from Q is
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Speed of train starting from Q = x kmph
∴ Speed of train starting from P = (x + 8) kmph
According to the question,
PR + RQ = PQ
⇒ (x + 8) × 6 + x × 6 = 162
[Distance = Speed × Time]
⇒ 6x + 48 + 6x = 162
⇒ 12x = 162 – 48 = 114⇒ x = 114 = 19 12 2 = 9 1 kmph 2 Correct Option: C
Speed of train starting from Q = x kmph
∴ Speed of train starting from P = (x + 8) kmph
According to the question,
PR + RQ = PQ
⇒ (x + 8) × 6 + x × 6 = 162
[Distance = Speed × Time]
⇒ 6x + 48 + 6x = 162
⇒ 12x = 162 – 48 = 114⇒ x = 114 = 19 12 2 = 9 1 kmph 2
- P and Q starting simultaneously from two different places proceed towards each other at a speed of 20 km/hour and 30 km/hour respectively. By the time they meet each other. Q has covered 36 km more than that of P. The distance (in km.) between the two places is
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Let P and Q meet after t hours.
Distance = speed × time
According to the question,
30t – 20t = 36
⇒ 10t = 36⇒ t = 36 = 3.6 hours 10
∴ Distance between P and Q
= 30t + 20t
= 50t = (50 × 3.6) km.
= 180 km.
Second Method :
Here, a = 30, b = 20, d = 36Required distance = 
a + b 
× d a − b = 30 + 20 × 36 30 − 20 = 50 × 36 = 180 km 10 Correct Option: C
Let P and Q meet after t hours.
Distance = speed × time
According to the question,
30t – 20t = 36
⇒ 10t = 36⇒ t = 36 = 3.6 hours 10
∴ Distance between P and Q
= 30t + 20t
= 50t = (50 × 3.6) km.
= 180 km.
Second Method :
Here, a = 30, b = 20, d = 36Required distance = a + b × d a − b = 30 + 20 × 36 30 − 20 = 50 × 36 = 180 km 10
- Two trains X and Y start from Jodhpur to Jaipur and from Jaipur to Jodhpur respectively. After passing each other they take 4 hours 48 minutes and 3 hours 20 minutes to reach Jaipur and Jodhpur respectively. If X is moving at 45 km/hr, the speed of Y is
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Speed of X Speed of Y = √ Time taken by Y Time taken by X ⇒ 45 = √ 3 hours 20 min. y 4 hours 48 min. ⇒ 45 = √ 200 minutes y 288 minutes = 10 12
⇒ 10y = 12 × 45⇒ y = 12 × 45 = 54 kmph 10 Correct Option: C
Speed of X Speed of Y = √ Time taken by Y Time taken by X ⇒ 45 = √ 3 hours 20 min. y 4 hours 48 min. ⇒ 45 = √ 200 minutes y 288 minutes = 10 12
⇒ 10y = 12 × 45⇒ y = 12 × 45 = 54 kmph 10
- A train running at the speed of 84 km/hr passes a man walking in opposite direction at the
speed of 6 km/hr in 4 seconds. What is the length of train (in metre) ?
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Relative speed = (84 + 6) = 90 kmph
= 90 × 5 m/sec. 18
= 25 m/sec.
∴ Length of train
= Relative speed × Time
= 25 × 4 = 100 metreCorrect Option: C
Relative speed = (84 + 6) = 90 kmph
= 90 × 5 m/sec. 18
= 25 m/sec.
∴ Length of train
= Relative speed × Time
= 25 × 4 = 100 metre
- Two trains, each of length 125 metre, are running in parallel tracks in opposite directions. One train is running at a speed 65 km/hour and they cross each other in 6 seconds. The speed of the other train is
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Total length of both trains = 250 metres
Let speed of second train =x kmph
Relative speed = (65 + x) kmph= (65 + x) × 5 m/sec 18 ∴ Time = Sum of length of trains Relative Speed ⇒ 6 = 250 (65 + x) × 5 18 ⇒ 6 × 5 × (65 + x) = 250 18 ⇒ 65 + x = 250 × 3 5
⇒ 65 + x = 150
⇒ x = 150 – 65 = 85 kmphCorrect Option: B
Total length of both trains = 250 metres
Let speed of second train =x kmph
Relative speed = (65 + x) kmph= (65 + x) × 5 m/sec 18 ∴ Time = Sum of length of trains Relative Speed ⇒ 6 = 250 (65 + x) × 5 18 ⇒ 6 × 5 × (65 + x) = 250 18 ⇒ 65 + x = 250 × 3 5
⇒ 65 + x = 150
⇒ x = 150 – 65 = 85 kmph
