A jogger is running at a speed of 15 km/hr. In what time he will cross a track of length 400 meters?

Options

A. 110 sec
B. 104 sec
C. 100 sec
D. 96 sec

Answer

To solve the problem of how long it will take a jogger running at a speed of 15 km/hr to cross a track of length 400 meters, we can follow these steps:

### Step 1: Convert speed from km/hr to m/s
The speed given is in kilometers per hour (km/hr), and we need to convert it to meters per second (m/s) because the distance is given in meters.

1. **Conversion formula**:
\[ \text{Speed in m/s} = \text{Speed in km/hr} \times \frac{1000 \text{ m}}{1 \text{ km}} \times \frac{1 \text{ hr}}{3600 \text{ s}} \]

2. **Substituting the value**:
\[ \text{Speed in m/s} = 15 \times \frac{1000}{3600} \]

3. **Calculating**:
\[ \text{Speed in m/s} = 15 \times \frac{1000}{3600} = 15 \times \frac{5}{18} = \frac{75}{18} = \frac{25}{6} \text{ m/s} \]

### Step 2: Use the formula to calculate time
Now that we have the speed in meters per second, we can use the formula for time:

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

1. **Substituting the values**:
\[ \text{Distance} = 400 \text{ meters} \]
\[ \text{Speed} = \frac{25}{6} \text{ m/s} \]
\[ \text{Time} = \frac{400}{\frac{25}{6}} \]

2. **Calculating**:
\[ \text{Time} = 400 \times \frac{6}{25} = \frac{2400}{25} = 96 \text{ seconds} \]

### Final Answer
The jogger will take **96 seconds** to cross the track of length 400 meters.

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