Train Problems Complex Examples

In this class, We discuss Train Problems Complex Examples.

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Example 1:

Two stations, A and B, are 110 kilometers apart on a straight line.

One train starts at station A at 7 am and travels towards B at 20 kmph.

Another train starts at station B at 8 am and moves towards A at 25 kmph.

At what time will they meet?

Solution:

The below diagram shows the graphical intuition of the example.

One train starts at 7 am, and another at 8 am, one hour after the first train.

Important: By the time the two trains met, they covered the distance between A and B. Key point explained during the formula.

Assume: They met x hours after 7 am.

The train starts at A and travels x hours; the train starts at B and travels x-1 hours.

Distance covered by train started at A = 20x

Distance covered by train started at B = 25(x-1).

The distance covered by both the trains before they met = 110.

20x + 25(x-1) = 110

x = 3

The train met at 10 am.

Example 2:

A train X starts from M at 4 pm and reaches G at 5 pm.

Another train, Y, starts from G at 4 pm and reaches M at 5:30 pm.

The two trains will cross each other at one time?

Solution:

The below diagram shows the graphical intuition of the example.

Assume: the distance is x.

Before the two trains meet, assume the two trains travel y hours.

Both trains cover a distance x before they meet.

The above three points help to solve the example.

Time by X to cover x distance is 1hr.

Time by Y to cover x distance is 3/2 hour.

Speed = Distance / Time

Speed of X = x/1 kmph

Speed of Y = x/(3/2) kmph.

Assume: They met y hours after 4 pm.

xy + 2xy/3 = x

y(1 + 2/3) = 1

y = 3/5 hour

y = 36 minutes.

They met at 4:36 minutes.