A hare, pursued by a grey-hound, is 50 of her own leaps ahead of him. While the hare takes 4 leaps the grey-hound takes 3 leaps. In one leap the hare goes 7/4 metres and the grey-hound 11/4 metres. In how many leaps will the grey-hound overtake the hare?

Answer

To solve the problem step by step, we will follow the information provided in the question and calculate the number of leaps the greyhound will take to overtake the hare.

### Step 1: Determine the speeds of the hare and the greyhound.
- The hare takes 4 leaps while the greyhound takes 3 leaps.
- In one leap, the hare covers \( \frac{7}{4} \) meters, and the greyhound covers \( \frac{11}{4} \) meters.

**Speed of the hare in one second:**
- In 4 leaps, the hare travels:
\[ 4 \times \frac{7}{4} = 7 \text{ meters} \]

**Speed of the greyhound in one second:**
- In 3 leaps, the greyhound travels:
\[ 3 \times \frac{11}{4} = \frac{33}{4} \text{ meters} \]

### Step 2: Calculate the speeds in meters per second.
- The hare's speed:
\[ \text{Speed of hare} = 7 \text{ meters per 4 leaps} = \frac{7}{4} \text{ meters per leap} \times \frac{1}{1} \text{ leap per second} = 7 \text{ meters per second} \]

- The greyhound's speed:
\[ \text{Speed of greyhound} = \frac{33}{4} \text{ meters per 3 leaps} = \frac{33}{4} \times \frac{1}{3} \text{ leaps per second} = \frac{11}{4} \text{ meters per second} \]

### Step 3: Calculate the initial distance between the hare and the greyhound.
- The hare is 50 leaps ahead. Since one leap of the hare is \( \frac{7}{4} \) meters:
\[ \text{Distance ahead} = 50 \times \frac{7}{4} = \frac{350}{4} = 87.5 \text{ meters} \]

### Step 4: Determine the relative speed.
- The greyhound is chasing the hare, so we calculate the relative speed:
\[ \text{Relative speed} = \text{Speed of greyhound} - \text{Speed of hare} = \frac{11}{4} - \frac{7}{4} = \frac{4}{4} = 1 \text{ meter per second} \]

### Step 5: Calculate the time taken for the greyhound to overtake the hare.
- Using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Relative speed}} = \frac{87.5}{1} = 87.5 \text{ seconds} \]

### Step 6: Calculate the number of leaps taken by the greyhound in that time.
- The greyhound takes 3 leaps per second:
\[ \text{Total leaps} = 87.5 \text{ seconds} \times 3 \text{ leaps/second} = 262.5 \text{ leaps} \]

Since the number of leaps must be a whole number, we round it to the nearest whole number, which is 263 leaps.

### Final Answer:
The greyhound will overtake the hare in **263 leaps**.

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