**Train Problems Shortcuts :**

In this section, we are going to see the shortcuts which are much required to solve train problems.

**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

**Shortcut 7 :**

Let the length of the train be "L" meters.

Distance traveled to pass a pole = L meters

**Shortcut 8 :**

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 9 :**

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 10 :**

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 11 :**

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 12 :**

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 13 :**

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

= Square root (q) : Square root (p)

**Shortcut 14 :**

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 15 :**

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

If you would like to know, how the above explained shortcuts are being used to solve problems on trains,

After having gone through the stuff given above, we hope that the students would have understood "Train Problems Shortcuts".

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