A can run 440 metres in 51 seconds and B in 55 seconds. By how many seconds will B win if he has 40 metres start ?

Options

A. 10 sec
B. 1 sec
C. 4 sec
D. Can't be determined

Answer

To solve the problem, we need to determine how long it takes for both A and B to complete their respective distances, taking into account that B has a 40-meter head start.

### Step 1: Calculate the speeds of A and B

1. **Speed of A**:
- Distance = 440 meters
- Time = 51 seconds
- Speed of A = Distance / Time = 440 m / 51 s = \( \frac{440}{51} \) m/s

2. **Speed of B**:
- Distance = 440 meters
- Time = 55 seconds
- Speed of B = Distance / Time = 440 m / 55 s = \( \frac{440}{55} \) m/s

### Step 2: Calculate the effective distance B has to run

Since B has a 40-meter head start, the distance B needs to run is:
- Effective distance for B = 440 meters - 40 meters = 400 meters

### Step 3: Calculate the time taken by B to run 400 meters

Using the speed of B calculated in Step 1:
- Time taken by B = Distance / Speed = 400 m / \( \frac{440}{55} \) m/s

To simplify:
- Time taken by B = 400 m * \( \frac{55}{440} \) s = \( \frac{400 \times 55}{440} \) s
- Time taken by B = \( \frac{22000}{440} \) s = 50 seconds

### Step 4: Calculate the time taken by A to run 440 meters

Using the speed of A calculated in Step 1:
- Time taken by A = 51 seconds (as given in the problem)

### Step 5: Determine the difference in time between A and B

Now, we need to find out how many seconds B will win by:
- Time difference = Time taken by A - Time taken by B
- Time difference = 51 seconds - 50 seconds = 1 second

### Final Answer
B will win by 1 second.

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