Question

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
1. 22.2 sec
2. 20 sec
3. 5 sec
4. 4.8 sec

Answer 1

Correct Answer - Option 4 : 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

∴ The bike rider will take 4.8 sec to cross the train completely.