Concept of “Train [ट्रेन]-04”

Question: Two trains of the same length but with different speeds pass a static pole in 4 seconds and 5 seconds respectively. In what time will they cross each other when they are moving in the same direction? [Ans. (b) 40 sec]

(a) 30 sec (b) 40 sec (c) 24 sec (d) 50 sec (e) None of these

Solution:                                                                                                                                                                         

Solution:

T₁: T₂ = 4 sec: 5 sec    

So, let S₁: S₂ = 5 m/s: 4 m/s

Length of each train = 4×5= 20 meter             

Distance = 20 m + 20 m = 40 m                                                                                    

Relative speed = 5 m/s – 4 m/s = 1 m/s                                                                                                  

Time = Distance/ speed = 40 m/ (1 m/s) = 40 sec Ans.      

Detailed Explanation:

Concept: "(i) When a train crosses an electric pole or a person, it describes a distance equal to its length. But, when a train crosses a platform or bridge; it describes a distance equal to the sum of the length of train and platform/bridge."

"(ii) When distances are the same, speeds are inversely proportional to their corresponding timings”

Here lengths of the trains are the same. So, speeds will be in the inverse ratio of corresponding timings.

Given that the time taken  by two trains of the same length in passing a static pole are respectively 4 seconds and 5 seconds. So, let the corresponding speeds of the trains are 5 m/s and 4 m/s.

Thus, the length of each train = 5 m/s × 4 sec = 20 meter.

When the two trains cross each other, the distance is 40 meter (20 + 20).

Again, since the two trains are moving in the same direction, so relative speed is 5 m/s – 4 m/s = 1 m/s

Time = 40 meter/1 m/s = 40 sec Ans.

Let the length of each train = 20 meter (4×5= 20; 4 sec is time and 5 m/s is corresponding speed)