The jogging track in a sports complex is 726 metres in circumference. Pradeep and his wife start from the same point and walk in opposite directions at 4.5 km/h and 3.75 km/h, respectively. They will meet for the first time in

Options

A. 5.5 min
B. 6.0 min
C. 5.28 min
D. 4.9 min

Answer

To solve the problem, we need to find out when Pradeep and his wife will meet for the first time while walking in opposite directions on a jogging track with a circumference of 726 meters.

### Step-by-step Solution:

1. **Convert Speeds from km/h to m/s**:
- Pradeep's speed: 4.5 km/h
- Wife's speed: 3.75 km/h
- To convert km/h to m/s, we use the conversion factor (1 km/h = 5/18 m/s).
- Pradeep's speed in m/s:
\[ 4.5 \times \frac{5}{18} = 1.25 \text{ m/s} \]
- Wife's speed in m/s:
\[ 3.75 \times \frac{5}{18} = 1.04167 \text{ m/s} \]

2. **Calculate the Relative Speed**:
- Since they are walking in opposite directions, we add their speeds to find the relative speed.
- Relative speed:
\[ 1.25 + 1.04167 = 2.29167 \text{ m/s} \]

3. **Calculate the Time to Meet**:
- They will meet when the distance covered equals the circumference of the track (726 meters).
- Using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
- Time to meet:
\[ \text{Time} = \frac{726}{2.29167} \approx 317.5 \text{ seconds} \]

4. **Convert Time from Seconds to Minutes**:
- To convert seconds to minutes, we divide by 60.
- Time in minutes:
\[ \text{Time in minutes} = \frac{317.5}{60} \approx 5.29 \text{ minutes} \]

### Final Answer:
Pradeep and his wife will meet for the first time in approximately **5.29 minutes**.

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