A can run 200 metres in 35 seconds and B in 38 seconds. By what distance can A beat B ?

Options

A. `(15) (11)/(19)`
B. `(15) (15)/(19)`
C. `(15) (5)/(19)`
D. None of these

Answer

To solve the problem of how far A can beat B, we can follow these steps:

### Step 1: Determine the speeds of A and B
First, we need to calculate the speeds of both A and B.

- **Speed of A** = Distance / Time = 200 meters / 35 seconds = \( \frac{200}{35} \) meters per second
- **Speed of B** = Distance / Time = 200 meters / 38 seconds = \( \frac{200}{38} \) meters per second

### Step 2: Calculate the time difference
Next, we find out how much longer B takes compared to A.

- **Time difference** = Time taken by B - Time taken by A = 38 seconds - 35 seconds = 3 seconds

### Step 3: Calculate the distance B covers in the time difference
Now, we need to find out how far B runs in the 3 seconds that it takes longer than A.

- Distance covered by B in 3 seconds = Speed of B × Time difference
- Distance covered by B in 3 seconds = \( \frac{200}{38} \) meters/second × 3 seconds

### Step 4: Simplify the calculation
Now, we will calculate the distance:

- Distance = \( \frac{200 \times 3}{38} = \frac{600}{38} \) meters
- Simplifying \( \frac{600}{38} \) gives us \( \frac{300}{19} \) meters

### Step 5: Finalize the answer
To find out by how much distance A beats B, we need to express the distance in a simpler form:

- A beats B by \( \frac{300}{19} \) meters, which can also be approximated as \( 15.79 \) meters.

Thus, the final answer is:
**A can beat B by \( \frac{300}{19} \) meters or approximately 15.79 meters.**