Two trains of lengths 80 m and 90 m are moving in opposite directions at 10 m/s and 7 m/s, respectively. Find the time taken by the trains to cross each other.

Answer

To solve the problem of finding the time taken by two trains to cross each other, we can follow these steps:

### Step 1: Identify the lengths of the trains
- Train 1 (T1) has a length of 80 meters.
- Train 2 (T2) has a length of 90 meters.

### Step 2: Identify the speeds of the trains
- Speed of Train 1 (S1) = 10 m/s
- Speed of Train 2 (S2) = 7 m/s

### Step 3: Calculate the relative speed of the trains
Since the trains are moving in opposite directions, the relative speed (S_relative) is the sum of their speeds:
\[ S_{\text{relative}} = S1 + S2 = 10 \, \text{m/s} + 7 \, \text{m/s} = 17 \, \text{m/s} \]

### Step 4: Calculate the total distance to be covered
To find the total distance that needs to be covered when the two trains cross each other, we add the lengths of both trains:
\[ \text{Total distance} = \text{Length of T1} + \text{Length of T2} = 80 \, \text{m} + 90 \, \text{m} = 170 \, \text{m} \]

### Step 5: Calculate the time taken to cross each other
Using the formula for time, which is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
we can substitute the total distance and the relative speed:
\[ \text{Time} = \frac{170 \, \text{m}}{17 \, \text{m/s}} = 10 \, \text{seconds} \]

### Conclusion
The time taken by the trains to cross each other is **10 seconds**.

---