Speed, Time and Distance
- The length of Lucknow mail is 120m and that of punjab mail is 80 m. These two trains are running in the same direction with velocities of 40 km/h and 50 km/h respectively. The time taken by them to cross each other is ?
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Time taken = Sum of length of the trains / Relative speed
Correct Option: B
Relative speed = 50 - 40 = 10 km/h = 50/18 m/s
∴ Time taken = Sum of length of the trains / Relative speed
= (200/50) x 18 = 72 sec.
- The average speed of a train in the onward journey is 25% more than that of the return journey. The train halts for one hour on reaching the destination. The total time taken for the complete to and fro journey is 17 h covering a distance of 800 km. The speed of the train in the onward journey, is ?
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Let the speed of the train during returning journey be x km/h
Speed during onward journey = x + 25x/100 = 5x/4 km/h.
Distance coverd in onward journey = 800 / 2 = 400 km
Total time taken = Covered distance / Speed
Time taken by train in onward journey = 400/5x/4
and time taken in returning journey = 400/x
Thus, 400/5x/4 + 400/x = 16
⇒ 320/x + 400/x + 16
Correct Option: D
Let the speed of the train during returning journey be x km/h
Speed during onward journey = x + 25x/100 = 5x/4 km/h.
Distance coverd in onward journey = 800 / 2 = 400 km
Total time taken = Covered distance / Speed
Time taken by train in onward journey = 400/(5x/4)
and time taken in returning journey = 400/x
Thus, 400/(5x/4) + 400/x = 16
⇒ 320/x + 400/x = 16
⇒ 16x = 720
∴ x = 45 km/h
Speed of the train in the onward journey = 5 x 45/4 = 56.25 km/h
- A dog starts chasing to a cat 2 hours later. It takes 2 hours to dog to catch the cat. If the speed of the dog is 30 Km/h. What is the speed of the cat?
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Time = Distance advanced / Relative speed
Correct Option: B
Time = Distance advanced / Relative speed
2 = 2x / (30 - x)
⇒ x = 15 km/h
- A car travels a distance of 840 km at uniform speed. If the speed of the car is 10 km/hr more. It takes two hours less to cover the same distance. The original speed of the car was ?
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Let the original speed be x km/hr.
Then, [ 840/x - 840/( x + 10) ] = 2Correct Option: C
Let the original speed be x km/hr.
Then, [ 840/x - 840/( x + 10) ] = 2
⇒ 840 (x + 10) - 840x = 2x (x+10)
⇒ x2 + 10x - 4200 = 0
⇒ (x + 70) (x - 60 ) = 0
∴ x = 60 km/hr.
- Two train start at the same time Aligarh and Delhi and processed toward each other at 16 km/hr and 21 km/hr respectively when they meet, it is found that one train has travelled 60 km more than the other. The distance between two station is ?
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Suppose they meet after y hours .
Then, 21y - 16y = 60Correct Option: B
Suppose they meet after y hours .
Then, 21y - 16y = 60
⇒ y = 12
∴required distance = (16 x 12 + 21 x 12) km.
= 444 km.
