Train Length Calculation: Bridge Crossing Problem

This problem involves calculating the train's length using the times it takes to cross two bridges of different lengths. We utilize the fundamental relationship: Distance = Speed × Time.

Define Variables

• Let $L$ be the length of the train (in meters).
• Let $S$ be the constant speed of the train (in m/s).

Formulate Equations

The total distance the train covers equals the bridge length plus the train length.

• For the 600 m bridge in 80 s: The equation is $600 + L = S \times 80$.
• For the 200 m bridge in 40 s: The equation is $200 + L = S \times 40$.

Calculate Train Length

Since the train's speed $S$ is constant, we can set up an equation by equating the expressions for $S$ derived from both scenarios:

From the first scenario: $S = \frac{600 + L}{80}$

From the second scenario: $S = \frac{200 + L}{40}$

Equating these speeds:

$ \frac{600 + L}{80} = \frac{200 + L}{40} $

To solve for $L$, we first simplify the equation by multiplying both sides by 40:

$ \frac{600 + L}{2} = 200 + L $

Next, we distribute the 2 on the left side:

$ 600 + L = 400 + 2L $

Now, we rearrange the terms to isolate $L$:

$ 600 - 400 = 2L - L $

Finally, we find the value of $L$:

$ L = 200 $

Conclusion

Therefore, the length of the train is 200 m.