A dog is chasing a rabbit. Initially distance between them is 400 leaps of dog. The time taken by dog to take 4 leaps is equal to 6 leaps taken by rabbit in that time. Rabbit covers 1.5 m in 1 leap and dog covers 2.5 m in 1 leap. In how many leaps will the dog catch the rabbit?

Answer

To solve the problem of how many leaps it will take for the dog to catch the rabbit, we can follow these steps:

### Step 1: Understand the initial conditions
- The initial distance between the dog and the rabbit is 400 leaps of the dog.

### Step 2: Determine the distance covered by each animal in one leap
- The rabbit covers 1.5 meters in one leap.
- The dog covers 2.5 meters in one leap.

### Step 3: Calculate the distance covered by each animal in a specific time frame
- The time taken by the dog to take 4 leaps is equal to the time taken by the rabbit to take 6 leaps.
- In this time frame:
- The dog covers:
\[ 4 \text{ leaps} \times 2.5 \text{ m/leap} = 10 \text{ meters} \]
- The rabbit covers:
\[ 6 \text{ leaps} \times 1.5 \text{ m/leap} = 9 \text{ meters} \]

### Step 4: Calculate the relative distance covered by the dog and rabbit
- The distance between them decreases by:
\[ 10 \text{ meters (dog)} - 9 \text{ meters (rabbit)} = 1 \text{ meter} \]

### Step 5: Convert the initial distance from leaps to meters
- The initial distance of 400 leaps of the dog in meters is:
\[ 400 \text{ leaps} \times 2.5 \text{ m/leap} = 1000 \text{ meters} \]

### Step 6: Calculate the time taken for the dog to catch the rabbit
- Since the distance between them decreases by 1 meter every time frame, to cover the total distance of 1000 meters:
\[ \text{Time frames required} = \frac{1000 \text{ meters}}{1 \text{ meter/frame}} = 1000 \text{ frames} \]

### Step 7: Calculate the number of leaps taken by the dog in that time
- In each time frame, the dog takes 4 leaps. Therefore, the total number of leaps taken by the dog is:
\[ 1000 \text{ frames} \times 4 \text{ leaps/frame} = 4000 \text{ leaps} \]

### Final Answer
The dog will catch the rabbit in **4000 leaps**.

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