At 7 : 00 am. I started travelling at the speed of 36 kmph. After I had travelled some distance, my car went out of order and I had to stop. After resting for 35 minutes, I returned home on foot at a speed of 14 kmph and reached home at 1 pm. Find the distance from my house at which my car broke down.

Answer

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

### Step 1: Determine the total time of the journey.
The person started traveling at 7:00 AM and reached home at 1:00 PM. The total time taken for the journey is:
\[ 1:00 \text{ PM} - 7:00 \text{ AM} = 6 \text{ hours} \]

### Step 2: Account for the resting time.
The person rested for 35 minutes, which is:
\[ 35 \text{ minutes} = \frac{35}{60} \text{ hours} = \frac{7}{12} \text{ hours} \]
Thus, the effective traveling time is:
\[ 6 \text{ hours} - \frac{7}{12} \text{ hours} = \frac{72}{12} - \frac{7}{12} = \frac{65}{12} \text{ hours} \]

### Step 3: Define variables for the journey.
Let \( x \) be the distance traveled before the car broke down, and let \( T \) be the time taken to travel this distance. The speed while going is 36 km/h, so:
\[ \text{Distance} = \text{Speed} \times \text{Time} \implies x = 36T \]

### Step 4: Determine the time taken to return home.
The time taken to return home on foot at a speed of 14 km/h is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{x}{14} \]

### Step 5: Set up the equation for total time.
The total time taken for the journey can be expressed as:
\[ T + \frac{x}{14} = \frac{65}{12} \]

### Step 6: Substitute \( x \) in the equation.
Substituting \( x = 36T \) into the equation:
\[ T + \frac{36T}{14} = \frac{65}{12} \]
This simplifies to:
\[ T + \frac{18T}{7} = \frac{65}{12} \]

### Step 7: Find a common denominator and simplify.
The common denominator for 1 and \( \frac{18T}{7} \) is 7:
\[ \frac{7T}{7} + \frac{18T}{7} = \frac{65}{12} \]
Combining the terms gives:
\[ \frac{25T}{7} = \frac{65}{12} \]

### Step 8: Cross-multiply to solve for \( T \).
Cross-multiplying gives:
\[ 25T \cdot 12 = 65 \cdot 7 \]
\[ 300T = 455 \]
\[ T = \frac{455}{300} = \frac{91}{60} \text{ hours} \]

### Step 9: Calculate the distance \( x \).
Now substitute \( T \) back to find \( x \):
\[ x = 36T = 36 \cdot \frac{91}{60} = \frac{3276}{60} = 54.6 \text{ km} \]

### Conclusion
The distance from the house at which the car broke down is:
\[ \boxed{54.6 \text{ km}} \]