Two trains of lengths 200 m and 150 m run on parallel tracks. When they run in the same direction, it will take 70 s to cross each other and when they run in opposite direction, they take 10 s to cross each other . Find the speed of the faster train

Answer

To solve the problem, we need to find the speeds of the two trains based on the information provided. Let's denote the speed of the faster train as \( S_f \) m/s and the speed of the slower train as \( S_s \) m/s.

### Step 1: Understanding the situation
When two trains cross each other, the total distance they need to cover is the sum of their lengths.

- Length of Train 1 (faster train) = 200 m
- Length of Train 2 (slower train) = 150 m
- Total length = 200 m + 150 m = 350 m

### Step 2: Crossing in the same direction
When the trains are moving in the same direction, the relative speed is the difference of their speeds. The time taken to cross each other is given as 70 seconds.

Using the formula:
\[ \text{Relative Speed} = \frac{\text{Total Distance}}{\text{Time}} \]
We can express this as:
\[ S_f - S_s = \frac{350 \text{ m}}{70 \text{ s}} = 5 \text{ m/s} \]
So, we have our first equation:
\[ S_f - S_s = 5 \quad \text{(1)} \]

### Step 3: Crossing in opposite directions
When the trains are moving in opposite directions, the relative speed is the sum of their speeds. The time taken to cross each other is given as 10 seconds.

Using the same formula:
\[ S_f + S_s = \frac{350 \text{ m}}{10 \text{ s}} = 35 \text{ m/s} \]
So, we have our second equation:
\[ S_f + S_s = 35 \quad \text{(2)} \]

### Step 4: Solving the equations
Now we have a system of two equations:
1. \( S_f - S_s = 5 \)
2. \( S_f + S_s = 35 \)

We can solve these equations simultaneously.

Adding both equations:
\[ (S_f - S_s) + (S_f + S_s) = 5 + 35 \]
This simplifies to:
\[ 2S_f = 40 \]
So,
\[ S_f = 20 \text{ m/s} \]

Now, substituting \( S_f \) back into equation (1) to find \( S_s \):
\[ 20 - S_s = 5 \]
This gives:
\[ S_s = 20 - 5 = 15 \text{ m/s} \]

### Conclusion
The speed of the faster train is \( 20 \text{ m/s} \).