A runs `1 3/4` times as fast as B. If A gives B a start of 60 metres. How far must the winning post be in order that A and B reach it at the same time ?

Options

A. 105 metres
B. 80 metres
C. 140 metres
D. 45 metres

Answer

To solve the problem, we need to determine the distance of the winning post such that both A and B reach it at the same time, given that A runs `1 3/4` times as fast as B and gives B a head start of 60 meters.

### Step-by-Step Solution:

1. **Define the Speeds of A and B:**
Let the speed of B be \( v \) meters per second. Then the speed of A is:
\[ \text{Speed of A} = \frac{7}{4} v \]

2. **Determine the Distance Covered by B:**
Let the distance to the winning post be \( d \) meters. Since B has a head start of 60 meters, the distance B needs to run is:
\[ \text{Distance for B} = d - 60 \]

3. **Set Up the Time Equation:**
The time taken by both A and B to reach the winning post must be the same. The time taken by A to cover distance \( d \) is:
\[ \text{Time for A} = \frac{d}{\frac{7}{4} v} = \frac{4d}{7v} \]
The time taken by B to cover distance \( d - 60 \) is:
\[ \text{Time for B} = \frac{d - 60}{v} \]

4. **Equate the Times:**
Since both A and B reach the winning post at the same time:
\[ \frac{4d}{7v} = \frac{d - 60}{v} \]

5. **Eliminate \( v \) from the Equation:**
Multiply both sides by \( 7v \) to eliminate \( v \):
\[ 4d = 7(d - 60) \]

6. **Expand and Simplify:**
Expanding the right side gives:
\[ 4d = 7d - 420 \]
Rearranging the equation:
\[ 420 = 7d - 4d \]
\[ 420 = 3d \]

7. **Solve for \( d \):**
Dividing both sides by 3:
\[ d = \frac{420}{3} = 140 \]

### Final Answer:
The distance of the winning post must be **140 meters**.