If Anita walks a certain distance at 13 km/hr, instead of 10 km/hr, she would walk 30 km more. The actual distance travelled by her is:

Options

A. 100 km
B. 50 km
C. 60 km
D. 25 km

Answer

To solve the problem, we need to determine the actual distance Anita traveled. Let's break it down step by step:

### Step 1: Understand the Problem
Anita walks a certain distance at two different speeds: 13 km/hr and 10 km/hr. When she walks at 13 km/hr, she covers 30 km more than when she walks at 10 km/hr.

### Step 2: Define Variables
Let the actual distance traveled by Anita be \( D \) kilometers.

### Step 3: Calculate Time Taken at Each Speed
- Time taken to walk distance \( D \) at 10 km/hr:
\[ \text{Time}_{10} = \frac{D}{10} \]
- Time taken to walk distance \( D + 30 \) km at 13 km/hr:
\[ \text{Time}_{13} = \frac{D + 30}{13} \]

### Step 4: Set Up the Equation
Since the time taken at both speeds must be equal (as she walks the same distance in both cases), we can set the two expressions for time equal to each other:
\[ \frac{D}{10} = \frac{D + 30}{13} \]

### Step 5: Cross Multiply to Solve for D
Cross-multiplying gives:
\[ 13D = 10(D + 30) \]
Expanding the right side:
\[ 13D = 10D + 300 \]

### Step 6: Rearrange the Equation
Now, we can rearrange the equation to isolate \( D \):
\[ 13D - 10D = 300 \]
\[ 3D = 300 \]

### Step 7: Solve for D
Dividing both sides by 3 gives:
\[ D = 100 \]

### Conclusion
The actual distance traveled by Anita is **100 kilometers**.

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