Two trains of lengths 70 m and 90 m are moving in opposite directions at 10 m/s and 6 m/s, respect- ively. Find the time taken by trains to cross each other.

Options

A. a. 10s
B. b. 8s
C. c. 12s
D. d. 16s

Answer

To find the time taken by two trains to cross each other, we can follow these steps:

### Step 1: Determine the lengths of the trains
- Length of Train 1 = 70 m
- Length of Train 2 = 90 m

### Step 2: Calculate the total distance to be covered when the trains cross each other
- Total distance = Length of Train 1 + Length of Train 2
- Total distance = 70 m + 90 m = 160 m

### Step 3: Determine the speeds of the trains
- Speed of Train 1 = 10 m/s
- Speed of Train 2 = 6 m/s

### Step 4: Calculate the relative speed of the trains
- Since the trains are moving in opposite directions, we add their speeds to find the relative speed.
- Relative speed = Speed of Train 1 + Speed of Train 2
- Relative speed = 10 m/s + 6 m/s = 16 m/s

### Step 5: Use the formula to find the time taken to cross each other
- The formula to calculate time is:
\[ \text{Time} = \frac{\text{Total Distance}}{\text{Relative Speed}} \]
- Substituting the values:
\[ \text{Time} = \frac{160 \text{ m}}{16 \text{ m/s}} = 10 \text{ seconds} \]

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

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