Two trains of lengths 75 m and 95 m are moving in the same direction at 9m/s and 8m/s, respectively. Find the time taken by the faster train to cross the slower train.

Answer

To solve the problem of finding the time taken by the faster train to cross the slower train, we can follow these steps:

### Step 1: Identify the lengths of the trains
- Length of Train 1 (T1) = 75 m
- Length of Train 2 (T2) = 95 m

### Step 2: Identify the speeds of the trains
- Speed of Train 1 (S1) = 9 m/s (faster train)
- Speed of Train 2 (S2) = 8 m/s (slower train)

### Step 3: Calculate the total distance to be covered
To find the distance that the faster train needs to cover to completely cross the slower train, we add the lengths of both trains:
- Total distance = Length of T1 + Length of T2
- Total distance = 75 m + 95 m = 170 m

### Step 4: Calculate the relative speed
Since both trains are moving in the same direction, the relative speed is the difference between their speeds:
- Relative Speed = Speed of T1 - Speed of T2
- Relative Speed = 9 m/s - 8 m/s = 1 m/s

### Step 5: Calculate the time taken to cross
Using the formula for time, which is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
we can now find the time taken by the faster train to cross the slower train:
- Time = Total Distance / Relative Speed
- Time = 170 m / 1 m/s = 170 seconds

### Final Answer
The time taken by the faster train to cross the slower train is **170 seconds**.

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