the faster train moving in opposite direc at 55km hr crosses passenger train of length 200m moving at 35kmhr in 18 secs length of faster train

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**.

---

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!

The faster train moving in opposite direction at 55 km/h crosses a passenger train of length 200 m moving at 35 km/h in 18 seconds. What is the length of the faster train?

Learn how to solve a relative speed problem where two trains are moving in opposite directions. The faster train, traveling at 55 km/h, crosses a passenger train of length 200 m moving at 35 km/h in 18 seconds. Detailed step-by-step solution with speed conversion and the time-distance formula. Suitable for students in Grades 9-10.

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