Speed, Time and Distance
- If a man walks at the rate of 5 km/hour, he misses a train by 7 minutes. However if he walks at the rate of 6 km/hour, he reaches the station 5 minutes before the arrival of the train. The distance covered by him to reach the station is
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Let the required distance be x km.
Difference of time = 7 + 5 = 12minutes = 1 hour 5 Time = Distance Speed
According to the question,x − x = 1 5 6 5 ⇒ 6x − 5x = 1 30 5 ⇒ x = 1 30 5 ⇒ x = 30 = 6 km. 5 Correct Option: D
Let the required distance be x km.
Difference of time = 7 + 5 = 12minutes = 1 hour 5 Time = Distance Speed
According to the question,x − x = 1 5 6 5 ⇒ 6x − 5x = 1 30 5 ⇒ x = 1 30 5 ⇒ x = 30 = 6 km. 5
- A train passes an electrical pole in 20 seconds and passes a platform 250 m long in 45 seconds. Find the length of the train.
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If the length of train be x metre,
then speed of train= x = x + 250 20 45 ⇒ x = x + 250 4 9
⇒ 9x = 4x + 1000
⇒ 9x – 4x = 1000
⇒ 5x = 1000⇒ x = 1000 = 200 metre 5 Correct Option: B
If the length of train be x metre,
then speed of train= x = x + 250 20 45 ⇒ x = x + 250 4 9
⇒ 9x = 4x + 1000
⇒ 9x – 4x = 1000
⇒ 5x = 1000⇒ x = 1000 = 200 metre 5
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is 25 minutes late. His usual time to cover this distance isWalking at 6 th of his usual speed a man 7
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Time and speed are inversely proportional.
∴ 7 × Usual time – Usual time = 25 minutes 6 ⇒ 
7 − 1 
= 25 minutes 6 ⇒ Usual time × 1 = 25 minutes 6
∴ Usual time = 25 × 6
= 150 minutes
= 2 hours 30 minutes
Second Method :
Here, A = 6, B = 7,t = 25 = 5 hrs. 60 12 Usual time = A × time Diff. of A and B = 6 × 5 = 5 hrs. (7 − 6) 12 2
= 2 hours 30 minutesCorrect Option: A
Time and speed are inversely proportional.
∴ 7 × Usual time – Usual time = 25 minutes 6 ⇒ 7 − 1 = 25 minutes 6 ⇒ Usual time × 1 = 25 minutes 6
∴ Usual time = 25 × 6
= 150 minutes
= 2 hours 30 minutes
Second Method :
Here, A = 6, B = 7,t = 25 = 5 hrs. 60 12 Usual time = A × time Diff. of A and B = 6 × 5 = 5 hrs. (7 − 6) 12 2
= 2 hours 30 minutes
- Two trains of lengths 150m and 180m respectively are running in opposite directions on parallel tracks. If their speeds be 50 km/hr and 58 km/hr respectively, in what time will they cross each other?
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Relative speed = (50 + 58) kmph
= 108 × 5 m/sec. 18
= 30 m/sec∴ Required time = Total length of trains Relative Speed = 150 + 180 seconds 30 = 330 seconds 30
= 11 secondsCorrect Option: D
Relative speed = (50 + 58) kmph
= 108 × 5 m/sec. 18
= 30 m/sec∴ Required time = Total length of trains Relative Speed = 150 + 180 seconds 30 = 330 seconds 30
= 11 seconds
- Two trains start at the same time from Aligarh and Delhi and proceed towards each other at the rate of 14 km and 21 km per hour respectively. When they meet, it is found that one train has travelled 70 km more than the other. The distance between two stations is
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Let the trains meet each other after t hours.
Distance = Speed × Time
According to the question,
21t – 14t = 70⇒ 7t = 70 ⇒ t = 70 = 10 hours 7
∴ Required distance
= 21t + 14t = 35t
= 35 × 10 = 350 km.
Second Method :
Here, a = 21, b = 14, d = 70Required distance = a + b × d a − b = 21 + 14 × 70 21 − 14 = 35 × 70 = 350 km. 7 Correct Option: A
Let the trains meet each other after t hours.
Distance = Speed × Time
According to the question,
21t – 14t = 70⇒ 7t = 70 ⇒ t = 70 = 10 hours 7
∴ Required distance
= 21t + 14t = 35t
= 35 × 10 = 350 km.
Second Method :
Here, a = 21, b = 14, d = 70Required distance = a + b × d a − b = 21 + 14 × 70 21 − 14 = 35 × 70 = 350 km. 7
