# TRAIN PROBLEMS SHORTCUTS

Shortcut 1 :

speed = distance/time

Shortcut 2 :

distance = speed ⋅ time

Shortcut 3 :

time = distance/speed

Shortcut 4 :

If the speed is given km per hour and we want to convert it in to meter per second, we have to multiply the given speed by 5/18.

Example :

90 km/hr = 90 ⋅ 5/18 = 25 meter/sec

Shortcut 5 :

If the speed is given meter per sec and we want to convert it in to km per hour, we have to multiply the given speed by 18/5.

Example :

25 meter/sec = 25 ⋅ 18/5 = 90 km/hr

Shortcut 6 :

Let the length of the train be L meters.

Distance traveled to pass a standing man = L meters

Distance traveled to pass a pole = L meters

Shortcut 7 :

Let the length of the train be 'a' meters and the length of the platform be 'b' meters.

Distance traveled to pass the platform is

= (a + b) meters

Shortcut 8 :

If two trains are moving on the same directions with speed of 'p' m/sec and 'q' m/sec (here p > q), then their relative speed is

= (p - q) m/sec

Shortcut 9 :

If two trains are moving opposite to each other in different tracks with speed of 'p' m/sec and 'q' m/sec,  then their relative speed is

= (p + q) m/sec

Shortcut 10 :

Let 'a' and 'b' are the lengths of the two trains.

They are traveling on the same direction with the speed 'p' m/sec and 'q' m/sec (here p > q), then the time taken by the faster train to cross the slower train

= (a + b)/(p - q) seconds

Shortcut 11 :

Let 'a' and 'b' are the lengths of the two trains.

They are traveling opposite to each other in different tracks with the speed 'p' m/sec and 'q' m/sec, then the time taken by the trains to cross each other

= (a + b)/(p + q) seconds

Shortcut 12 :

Two trains leave at the same time from the stations P and Q and moving towards each other.

After crossing, they take 'p' hours and 'q' hours to reach Q and P respectively.

Then the ratio of the speeds of two trains is √q : √p.

Shortcut 13 :

Two trains are running in the same direction/opposite direction.

The person in the faster train observes that he crosses the slower train in 'm' seconds.

Then the distance covered in "m" seconds in the relative speed is

= length of the slower train

Shortcut 14 :

Two trains are running in the same direction/opposite direction.

The person in the slower train observes that the faster train crossed him 'm' seconds.

Then the distance covered in 'm' seconds in the relative speed is

= length of the faster train

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