Two persons A and B start from the same location and walked around a square in opposite directions with constant speeds. The square has a side 60 m. Speed of A and B are `4 ms ^(-1) and 2 ms ^(-1)` respectively. When will they meet for the first time ?

Options

A. 30 s
B. 40 s
C. 10 s
D. 20 s

Answer

To solve the problem of when persons A and B will meet for the first time while walking around a square in opposite directions, we can follow these steps:

### Step 1: Calculate the perimeter of the square.
The perimeter \( P \) of a square is given by the formula:
\[ P = 4 \times \text{side length} \]
Given that the side length of the square is 60 m:
\[ P = 4 \times 60 = 240 \text{ m} \]

### Step 2: Determine the speeds of A and B.
- Speed of A, \( v_A = 4 \, \text{m/s} \)
- Speed of B, \( v_B = 2 \, \text{m/s} \)

### Step 3: Calculate the relative speed.
Since A and B are moving in opposite directions, their relative speed \( v_{relative} \) is the sum of their speeds:
\[ v_{relative} = v_A + v_B = 4 + 2 = 6 \, \text{m/s} \]

### Step 4: Use the formula to find the time taken to meet.
The time \( t \) taken to meet for the first time can be calculated using the formula:
\[ t = \frac{\text{Distance}}{\text{Relative Speed}} \]
Here, the distance they need to cover together to meet for the first time is the perimeter of the square:
\[ t = \frac{P}{v_{relative}} = \frac{240}{6} \]

### Step 5: Calculate the time.
Now we can compute the time:
\[ t = \frac{240}{6} = 40 \text{ seconds} \]

### Conclusion:
Persons A and B will meet for the first time after **40 seconds**.

---