In a circular race of 1200m, A and B start from the same point and at the same time with speeds of 27km/hr and 45km/hr respectively. Find when will they meet again for the first time on the track when they are running In the same direction

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Convert speeds from km/hr to m/s
- A's speed = 27 km/hr
- B's speed = 45 km/hr

To convert km/hr to m/s, we use the conversion factor \( \frac{5}{18} \).

For A:
\[ \text{Speed of A in m/s} = 27 \times \frac{5}{18} = 7.5 \text{ m/s} \]

For B:
\[ \text{Speed of B in m/s} = 45 \times \frac{5}{18} = 12.5 \text{ m/s} \]

### Step 2: Calculate the relative speed
Since A and B are running in the same direction, the relative speed is given by:
\[ \text{Relative Speed} = \text{Speed of B} - \text{Speed of A} = 12.5 \text{ m/s} - 7.5 \text{ m/s} = 5 \text{ m/s} \]

### Step 3: Determine the distance of the circular track
The distance of the circular track is given as 1200 meters.

### Step 4: Calculate the time taken to meet again
Using the formula for time, which is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} \]
we can substitute the values:
\[ \text{Time} = \frac{1200 \text{ m}}{5 \text{ m/s}} = 240 \text{ seconds} \]

### Conclusion
A and B will meet again for the first time on the track after **240 seconds**.

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