A dog sees a cat. It estimates that the cat is 25 leaps away. The cat sees the dog and starts running with the dog in hot pursuit. If in every minute, the dog makes 5 leaps and the cat makes 6 leaps and one leap of the dog is equal to 2 leaps of the cat. Find the time in which the cat is caught by the dog (assume an open field with no trees)

Options

A. 12 minutes
B. 15 minutes
C. 12.5 minutes
D. None of these

Answer

To solve the problem step-by-step, we will follow these calculations:

### Step 1: Understand the distances and speeds
- The dog estimates that the cat is **25 leaps away**.
- The dog makes **5 leaps per minute**.
- The cat makes **6 leaps per minute**.
- One leap of the dog is equal to **2 leaps of the cat**.

### Step 2: Convert the cat's speed to dog leaps
Since one leap of the dog equals two leaps of the cat, we can convert the cat's speed into dog leaps:
- The cat's speed in dog leaps = \( \frac{6 \text{ cat leaps}}{2} = 3 \text{ dog leaps per minute} \).

### Step 3: Calculate the relative speed
Now, we need to find the relative speed between the dog and the cat:
- Speed of the dog = **5 dog leaps per minute**.
- Speed of the cat = **3 dog leaps per minute**.
- Since both are moving in the same direction, the relative speed of the dog with respect to the cat is:
\[ \text{Relative Speed} = \text{Speed of Dog} - \text{Speed of Cat} = 5 - 3 = 2 \text{ dog leaps per minute}. \]

### Step 4: Calculate the time taken to catch the cat
To find the time taken for the dog to catch the cat, we can use the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}}. \]
Here, the distance is **25 dog leaps** and the relative speed is **2 dog leaps per minute**:
\[ \text{Time} = \frac{25 \text{ dog leaps}}{2 \text{ dog leaps per minute}} = 12.5 \text{ minutes}. \]

### Conclusion
The time taken for the dog to catch the cat is **12.5 minutes**.

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