Two persons start running towards each other from two points that arc 120m apart. First person ruins with a speed of `5ms^(-1)` and the other wi9th a speed of `7ms^(-1)`. Both the persons meet after

Options

A. 10 s
B. 24 s
C. 1 min
D. 48 s

Answer

To solve the problem of two persons running towards each other from two points that are 120 meters apart, we can follow these steps:

### Step 1: Identify the speeds of both persons
- Let the speed of the first person (Person A) be \( v_A = 5 \, \text{m/s} \).
- Let the speed of the second person (Person B) be \( v_B = 7 \, \text{m/s} \).

### Step 2: Calculate the relative speed
Since both persons are running towards each other, we can add their speeds to find the relative speed:
\[ v_{\text{relative}} = v_A + v_B = 5 \, \text{m/s} + 7 \, \text{m/s} = 12 \, \text{m/s} \]

### Step 3: Use the distance formula to find the time taken to meet
We know the total distance between them is 120 meters. We can use the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
Substituting the values we have:
\[ \text{Time} = \frac{120 \, \text{m}}{12 \, \text{m/s}} = 10 \, \text{s} \]

### Conclusion
Both persons will meet after **10 seconds**.

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