A camel pursue an elephant and takes 5 leaps for every 7 leaps of the elephant, but 6 leaps of elephant are equal to 3 leaps of camel. What is the ratio of speed of camel and elephant?

Answer

To find the ratio of the speed of the camel to the speed of the elephant, we need to analyze the information given in the problem step by step.

### Step 1: Understand the leap relationship
We know that:
- The camel takes 5 leaps for every 7 leaps of the elephant.

### Step 2: Establish the distance relationship
We are also given that:
- 6 leaps of the elephant are equal to 3 leaps of the camel.

From this, we can derive the distance covered by each leap.

### Step 3: Calculate the distance of each leap
Let the distance of one leap of the elephant be \( d_e \) and the distance of one leap of the camel be \( d_c \).

From the information given:
- \( 6 \times d_e = 3 \times d_c \)

This simplifies to:
- \( d_c = \frac{6}{3} \times d_e = 2 \times d_e \)

So, the distance of one leap of the camel is twice the distance of one leap of the elephant.

### Step 4: Calculate the total distance covered in a common number of leaps
Now, let’s consider the distances covered by both animals in a common scenario.

If the elephant takes 7 leaps, the distance covered by the elephant is:
- Distance by elephant = \( 7 \times d_e \)

In the same time, the camel takes 5 leaps, so the distance covered by the camel is:
- Distance by camel = \( 5 \times d_c = 5 \times (2 \times d_e) = 10 \times d_e \)

### Step 5: Calculate the speeds
Now we can find the speeds of both animals. Speed is defined as distance per unit time. Since both animals are taking leaps in the same time frame, we can compare their distances directly.

- Speed of elephant \( (S_e) \) = Distance covered by elephant / Time taken = \( 7 \times d_e \)
- Speed of camel \( (S_c) \) = Distance covered by camel / Time taken = \( 10 \times d_e \)

### Step 6: Find the ratio of speeds
Now, we can find the ratio of the speeds of the camel to the elephant:
\[ \text{Ratio of speeds} = \frac{S_c}{S_e} = \frac{10 \times d_e}{7 \times d_e} = \frac{10}{7} \]

### Final Answer
Thus, the ratio of the speed of the camel to the speed of the elephant is:
\[ \text{Ratio of speed of camel to speed of elephant} = \frac{10}{7} \]

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