You arrive at your school 5 minutes late if you walk with a speed of 4km/h, but you arrive 10 minutes before the scheduled time If you walk with a speed of 5 km/h. The distance of your school from your house (in km) is

Options

A. 4
B. 5
C. 10
D. 2

Answer

To solve the problem, we need to determine the distance from your house to your school based on the information given about your walking speeds and the times you arrive.

### Step-by-Step Solution:

1. **Define Variables**:
Let the distance from your house to your school be \( x \) kilometers.

2. **Set Up Time Equations**:
- When walking at a speed of 4 km/h, you arrive 5 minutes late. This means you take longer than the scheduled time.
- When walking at a speed of 5 km/h, you arrive 10 minutes early. This means you take less time than the scheduled time.

3. **Convert Minutes to Hours**:
- 5 minutes = \( \frac{5}{60} \) hours = \( \frac{1}{12} \) hours.
- 10 minutes = \( \frac{10}{60} \) hours = \( \frac{1}{6} \) hours.

4. **Express Time Taken**:
- The time taken to walk to school at 4 km/h is \( \frac{x}{4} \) hours.
- The time taken to walk to school at 5 km/h is \( \frac{x}{5} \) hours.

5. **Set Up the Equation**:
The difference in time taken at the two speeds can be expressed as:
\[ \frac{x}{4} - \frac{x}{5} = \frac{1}{12} + \frac{1}{6} \]

6. **Find a Common Denominator**:
The common denominator for the left side (4 and 5) is 20:
\[ \frac{5x}{20} - \frac{4x}{20} = \frac{1}{12} + \frac{1}{6} \]
This simplifies to:
\[ \frac{x}{20} = \frac{1}{12} + \frac{2}{12} = \frac{3}{12} = \frac{1}{4} \]

7. **Solve for x**:
Now we can set up the equation:
\[ \frac{x}{20} = \frac{1}{4} \]
Cross-multiplying gives:
\[ x = 20 \times \frac{1}{4} = 5 \]

8. **Conclusion**:
The distance from your house to your school is \( x = 5 \) kilometers.

### Final Answer:
The distance of your school from your house is **5 kilometers**.