A train running with a constant speed of 80 km/h. A bike rider is just at the middle of the train and start chasing the train at 100 km/h. he crossed the train completely after 21.6 sec. In how many sec. he will cross the train completely, when they are running opposite to each other

A train running with a constant speed of 80 km/h. A bike rider is just at the middle of the train and start chasing the train at 100 km/h. he crossed the train completely after 21.6 sec. In how many sec. he will cross the train completely, when they are running opposite to each other Correct Answer 4.8 sec

Given:

Speed of train = 80 km/h and speed of bike rider = 100 km/h

Time taken to cross the train = 21.6 sec (From middle of the train)

Formula used:

Time = Distance/Speed

Concept used:

1.) Relative Speed = Speed of one object with respect to other object

2.) When two object of Speed V₁ and V₂, respectively travels in same direction then the relative speed = |V₁ – V₂|

3.) When two object of Speed V₁ and V₂, respectively travels in opposite direction then the relative Speed = |V₁ + V₂|

4.) When any object crosses the train, then the distance travelled by that object would be the length of the train.

5.) m/s = (Km/h) × 5/18

Calculations:

Relative speed = 100 – 80 = 20 km/h = 20 × 5/18 m/sec

Time taken = 21.6 sec

Distance = (100/18) × 21.6 = 120 m

Let the length of train be L

According to the question,

⇒ 120 m = L/2

⇒ L = 240 m

Now, they are running opposite to each other

Relative speed = 100 + 80 = 180 km/h = 180 × 5/18 m/sec

Distance = 240 m

Time = 240/50 = 24/5 sec