A student walks from his house at 6.30 am and reaches his school at 7:15 am. The distance of the school from his house is 6 km. The speed of the student is

Options

A. `4(1)/(2)` km/h
B. 8 km/h
C. 6 km/h
D. 4 km/h

Answer

To find the speed of the student, we can follow these steps:

### Step 1: Determine the total time taken to walk to school
The student leaves his house at 6:30 AM and arrives at school at 7:15 AM.

- From 6:30 AM to 7:00 AM is 30 minutes.
- From 7:00 AM to 7:15 AM is an additional 15 minutes.

So, the total time taken is:
\[ 30 \text{ minutes} + 15 \text{ minutes} = 45 \text{ minutes} \]

### Step 2: Convert the time from minutes to hours
Since speed is usually expressed in kilometers per hour (km/h), we need to convert the time taken into hours.

To convert 45 minutes into hours:
\[ \text{Time in hours} = \frac{45 \text{ minutes}}{60} = 0.75 \text{ hours} \]

### Step 3: Use the formula for speed
The formula for speed is given by:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

### Step 4: Substitute the values into the formula
The distance from the house to the school is 6 km, and the time taken is 0.75 hours.

So, substituting the values:
\[ \text{Speed} = \frac{6 \text{ km}}{0.75 \text{ hours}} \]

### Step 5: Calculate the speed
Now, we perform the calculation:
\[ \text{Speed} = \frac{6}{0.75} = 8 \text{ km/h} \]

Thus, the speed of the student is **8 kilometers per hour**.

### Summary of the Solution:
1. Total time taken: 45 minutes
2. Time in hours: 0.75 hours
3. Speed formula: Speed = Distance / Time
4. Substitute values: Speed = 6 km / 0.75 hours
5. Calculate speed: Speed = 8 km/h

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