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The distance between two stations A and B is 107 km. A 1.8 km long train starts from station A for station B at a speed of 90 km/h. After 10 minutes, another train, 1.2 km long, starts from station B and runs towards station A at a speed of 100 km/h. What is the distance of the point from station A where the two trains pass each other?

The distance between two stations A and B is 107 km. A 1.8 km long train starts from station A for station B at a speed of 90 km/h. After 10 minutes, another train, 1.2 km long, starts from station B and runs towards station A at a speed of 100 km/h. What is the distance of the point from station A where the two trains pass each other? Correct Answer 58.2 km

Given:

Distance between two stations is 107km.

Length and Speed of first train is 1.8km and 90km/hr respectively.

Length and Speed of another train is 1.2km and 100km/hr respectively. 

Formula Used:

Speed = Distance/Time,

Relative speed when running opposite = Distance/Sum of the speed of both the trains

Calculation:

First train ran for 10 minutes, 

In 10 minutes, train will cover,

⇒ 90 × 10/60

⇒ 15 km

Actual distance to cover now,

⇒ 107 – 92

⇒ 92 km

Now both trains are running in opposite direction,

⇒ Relative speed = 100 + 90

⇒ Ralative speed = 190 km/hr

Time required to cross = Distance to cover/Relative speed

⇒ Time taken = 95/190

⇒ Time taken = 1/2 hr

In 1/2 hr first train will cover,

⇒ 1/2 × 90

⇒ 45km

So the total distance covered by first train till now is,

⇒ 15 + 45

⇒ 60 km.

Actual distance covered i.e. end point of a train will at,

⇒  Distance covered – length of a first train

⇒ 60 – 1.8

⇒ 58.2km

∴ Total distance covered from point A is 58.2 km.

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