A dog starts chasing to a cat 2 hours later it takes 2 hours to dog to catch the cat.if the speed of the dog is 30 km/h what is the speed of the cat?

A. 10 km/hr
B. 165 km/hr
C. 20 km/hr
D. can't be determined

Options

A. 10 km/hr
B. 15 km/hr
C. 20 km/hr
D. can't be determined

Answer

To solve the problem, we need to determine the speed of the cat based on the information provided about the dog chasing the cat. Let's break down the solution step by step.

### Step-by-Step Solution:

1. **Understand the Problem**:
- A dog starts chasing a cat after 2 hours.
- It takes the dog 2 hours to catch the cat.
- The speed of the dog is 30 km/h.

2. **Define Variables**:
- Let the speed of the cat be \( x \) km/h.

3. **Calculate the Distance Traveled by the Cat**:
- The cat runs for a total of 4 hours (2 hours before the dog starts chasing and 2 hours while the dog is chasing).
- Therefore, the distance traveled by the cat in 4 hours is:
\[ \text{Distance}_{\text{cat}} = 4x \text{ km} \]

4. **Calculate the Distance Traveled by the Dog**:
- The dog runs for 2 hours while chasing the cat.
- The distance traveled by the dog in 2 hours is:
\[ \text{Distance}_{\text{dog}} = 2 \times 30 = 60 \text{ km} \]

5. **Set Up the Equation**:
- Since the dog catches the cat, the distances traveled by both the dog and the cat must be equal at the moment of catching:
\[ 4x = 60 \]

6. **Solve for \( x \)**:
- Rearranging the equation gives:
\[ x = \frac{60}{4} = 15 \text{ km/h} \]

7. **Conclusion**:
- The speed of the cat is \( 15 \) km/h.

### Final Answer:
The speed of the cat is **15 km/h**. However, this option is not listed in the choices provided.