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?

Options

A. 10 km/h
B. 15 km/h
C. 20 km/h
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 and the time taken for the dog to catch the cat.

### Step-by-Step Solution:

1. **Understand the Problem**:
- The dog starts chasing the cat 2 hours after the cat has already started moving.
- The dog catches the cat 2 hours after it starts chasing.
- The speed of the dog is given as 30 km/h.

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

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

4. **Calculate the Distance the Dog Travels**:
- The dog travels for 2 hours at a speed of 30 km/h.
- Therefore, the distance traveled by the dog is:
\[ \text{Distance}_{\text{dog}} = \text{Speed}_{\text{dog}} \times \text{Time}_{\text{dog}} = 30 \times 2 = 60 \text{ km} \]

5. **Set Up the Equation**:
- Since the dog catches the cat, the distances traveled by both are equal when the dog catches the cat:
\[ 4x = 60 \]

6. **Solve for \( x \)**:
- To find the speed of the cat, we solve the equation:
\[ x = \frac{60}{4} = 15 \text{ km/h} \]

### Final Answer:
The speed of the cat is **15 km/h**.