A rabit takes 22 leaps for every 17 leaps of cat and 22 leaps of a rabit are equal to 17 leaps of the cat. What is the ratio of the speeds of rabit and cat?

Options

A. 0.042361111111111
B. 484:289
C. 0.72361111111111
D. none of these

Answer

To find the ratio of the speeds of a rabbit and a cat based on the information given, we can follow these steps:

### Step 1: Understand the relationship between leaps
We know that:
- A rabbit takes 22 leaps for every 17 leaps of a cat.
- The distance covered in 22 leaps of the rabbit is equal to the distance covered in 17 leaps of the cat.

### Step 2: Define the distance covered in leaps
Let’s denote:
- The distance covered in one leap of the rabbit as \( d_r \).
- The distance covered in one leap of the cat as \( d_c \).

From the information given:
- The distance covered in 22 leaps of the rabbit is \( 22 \times d_r \).
- The distance covered in 17 leaps of the cat is \( 17 \times d_c \).

### Step 3: Set up the equation based on distances
Since the distances are equal:
\[ 22 \times d_r = 17 \times d_c \]

### Step 4: Express the distances in terms of each other
From the equation above, we can express the distance of the rabbit in terms of the cat:
\[ \frac{d_r}{d_c} = \frac{17}{22} \]

### Step 5: Calculate the speeds
Speed is defined as distance per unit time. Since the time taken for each leap is the same for both animals, we can say:
- Speed of the rabbit \( v_r = d_r \)
- Speed of the cat \( v_c = d_c \)

### Step 6: Find the ratio of speeds
Using the ratio of distances:
\[ \frac{v_r}{v_c} = \frac{d_r}{d_c} = \frac{17}{22} \]

### Step 7: Write the final answer
Thus, the ratio of the speeds of the rabbit to the cat is:
\[ \text{Ratio of speeds} = \frac{17}{22} \]