A dog takes 3 leaps for every 5 leaps of a hare. If one leap of the dog is equal to 3 leaps of the hare, the ratio of the speed of the dog to that of the hare is :

Options

A. A) 9:5
B. B) 2:3
C. C) 4:7
D. D) 5:6

Answer

To solve the problem, we need to find the ratio of the speed of the dog to the speed of the hare based on the given information.

### Step-by-Step Solution:

1. **Understand the leaps**:
- The dog takes 3 leaps for every 5 leaps of the hare. This means that in the same time period, the dog covers 3 leaps while the hare covers 5 leaps.

2. **Convert leaps to distance**:
- We know that one leap of the dog is equal to 3 leaps of the hare. Therefore, the distance covered by the dog in one leap can be expressed in terms of the hare's leaps.
- If one leap of the dog = 3 leaps of the hare, then:
- Distance covered by the dog in 3 leaps = 3 leaps * 3 (leaps of hare per leap of dog) = 9 leaps of the hare.

3. **Calculate the total distance covered**:
- In the same time frame, the hare covers 5 leaps.
- So, in the time it takes for the dog to take 3 leaps, the hare takes 5 leaps.

4. **Set up the ratio of distances**:
- Distance covered by the dog in 3 leaps = 9 leaps of the hare.
- Distance covered by the hare in 5 leaps = 5 leaps of the hare.
- The ratio of the distance covered by the dog to the distance covered by the hare is:
\[ \text{Ratio of distances} = \frac{9 \text{ (dog's distance)}}{5 \text{ (hare's distance)}} = \frac{9}{5} \]

5. **Calculate the ratio of speeds**:
- Speed is defined as distance per unit time. Since both the dog and the hare take the same amount of time to complete their respective leaps, the ratio of their speeds will be the same as the ratio of the distances they cover.
- Thus, the ratio of the speed of the dog to the speed of the hare is:
\[ \text{Speed ratio} = \frac{9}{5} \]

### Final Answer:
The ratio of the speed of the dog to that of the hare is \( \frac{9}{5} \).