Time Speed Distance formulas, tricks, shortcuts, time Speed and distance problems.

Time, Speed & Distance  formulas, tricks :
Time, Speed & Distance

Some important formulae :
  1. Distance = Time × Speed
  2. Speed = Distance / Time.
  3. Time = Distance / Speed.
Important facts :
  1. If two objects move parallel in the same direction, then their  relative speed is equal to the difference of their movements.
  2. If two objects move in a parallel opposite direction, then their relative speed is equal to the sum of their movements.
  3. When converting km/hr to meters/ second, multiply by 5/18.
  4. When converting meters/second to km/hr, multiply by 18/5.
  5. The sum of the speed opposite the direction of the train should be added.
  6. If the direction of the train is the same, the speed should be subtracted.
  7. In mathematics, add up all the long distance and calculate the distance to the total lobby.
  8. If a person covers a certain distance at a speed of X km/hr and an equal distance with Y km/hr, then the average speed for the entire journey = ( 2XY ) / (X + Y ) km/hr
  9. If the boat moves in the direction of water flow, then Total speed of boat = speed of boat in water + Drift of water.
  10. If the boat moves in the opposite direction to the flow of water. Then, Total speed of boat = speed of boat in still water - speed of water flow.
  11. If the speed in the direction of the current of a boat is X km/hr and the speed in the opposite direction of the stream is Y km/hr. Then, 
  12. Boat move in quite water = 1/2 (X + Y ) km/hr.
  13. Stream velocity = 1/2 (X - Y) km/hr.
Examples :
1. If a train travels at a speed of 72 km/hr, find it's speed in meters/second.
Ans. :
When converting km/hr to meters/second multiply by 5/18.
Therefore, speed = 72 × ( 5 / 18 ) = 20 meters/ second.

2. If a train travels at a speed of 108 km/hr, find it's speed in meters/second.
Ans. :
Speed = 108 × ( 5 / 18 ) = 30 meters/ second.

3. If a train travels at a speed of 20 meters/second, find it's speed in km/hr.
Ans. :
When converting meters/second to km/hr, multiply by 18/5.
Therefore, speed = 20 × ( 18 / 5 ) = 72 km/hr.

4. If a train travels at a speed of 30 meters/second. Find it's speed in km/hr.
Ans. :
Speed = 30 × ( 18 / 5 ) = 108 km/hr.

5. If a train crosses a pole at a speed of 90 km/hr in 10 seconds, find the length of the train.
Ans. :
Distance = Speed × Time
                 = 90 × ( 5 / 18 ) × 10
                 = 250 
Therefore, Length of Railway = 250 meters.

6. How long will it take for a 300 meters long train to cross a pole at a speed of 72 km/hr.
Ans. :
Speed = 72 × ( 5 / 18 ) = 20 meters/second.
Time = Distance / Speed
           = 300 / 20
           = 15 seconds.

7. How long will it take for a 300 meters long train to cross a 200 meters long bridge at a speed of 90km/hr?
Ans. :
Distance = 300 + 200 = 500 meters.
Speed = 90 × ( 5 / 18 ) = 25 meters/ second.
Time = Distance / Speed
          = 500 / 25
          = 20 seconds.

8. A 250 meters long train crosses a tunnel at 72 km/hr speed in 30 seconds. What is the length of the tunnel?
Ans. :
Suppose, length of tunnel = x       
In mathematics, add up all the long distance and calculate the distance to the total lobby.
Therefore, Distance = x + 250
Now,
Distance = Speed × Time
x + 250 = 72 × ( 5 / 18 ) × 30
x + 250 = 20 × 30.
x + 250 = 600
x = 600 - 250
x = 350
Therefore, Length of tunnel = 350 meters.

9. What is the average speed of a train when a train travels from Kolhapur to Pune at a speed of 40 km/ hr and returns from Pune to Kolhapur at a speed of 60 km/hr?
Ans. :
Average Speed = 2xy / ( x + y ).
x = first speed = 40 km/hr.
y= second speed = 80 km/hr.
Therefore, Average Speed = ( 2 × 40 × 60 ) / ( 40 + 60 )

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