To solve this problem, we need to determine the length of the faster train. Both trains are moving in opposite directions, so their relative speed will be the sum of their individual speeds. Here's the step-by-step process:

Given:

• Speed of the faster train $S_f = 55 \, \text{km/h}$
• Speed of the passenger train $S_p = 35 \, \text{km/h}$
• Length of the passenger train $L_p = 200 \, \text{m}$
• Time taken to cross each other $t = 18 \, \text{seconds}$

Step 1: Convert speeds to meters per second

Since speeds are given in kilometers per hour, we need to convert them to meters per second:

$S_f = 55 \, \text{km/h} = \frac{55 \times 1000}{3600} = 15.28 \, \text{m/s}$ $S_p = 35 \, \text{km/h} = \frac{35 \times 1000}{3600} = 9.72 \, \text{m/s}$

Step 2: Calculate the relative speed

Since the trains are moving in opposite directions, their relative speed is the sum of their individual speeds:

$\text{Relative Speed} = S_f + S_p = 15.28 \, \text{m/s} + 9.72 \, \text{m/s} = 25 \, \text{m/s}$

Step 3: Use the formula to find the length of the faster train

The total distance covered by the relative motion in the time $t = 18 \, \text{seconds}$ is the sum of the lengths of both trains:

$\text{Distance covered} = \text{Relative Speed} \times \text{Time} = 25 \, \text{m/s} \times 18 \, \text{seconds} = 450 \, \text{meters}$

Let the length of the faster train be $L_f$. The total distance covered is the sum of the lengths of both trains:

$L_f + L_p = 450 \, \text{meters}$

Substituting the length of the passenger train:

$L_f + 200 = 450$

Step 4: Solve for the length of the faster train

$L_f = 450 - 200 = 250 \, \text{meters}$

Final Answer:

The length of the faster train is 250 meters.

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Would you like more details or have any further questions?

Here are 5 related questions:

1. How would the scenario change if both trains moved in the same direction?
2. What happens to the relative speed if the slower train stops?
3. How would you calculate the time taken to cross if the faster train's speed changes?
4. Can you calculate the length of the passenger train if only the faster train's length and speed are known?
5. What if one of the trains was stationary, how does the crossing time change?

Tip: Always convert speeds into the same units before doing any calculations involving time and distance!