**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".

Apart from the stuff given above, if you want to know more about "Train Problems Shortcuts", please click here

Apart from the stuff "Word problems on fractions", if you need any other stuff in math, please use our google custom search here.

Widget is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Time and work word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**