In a 400 m race ,A runs at a speed of 16m/s. If A gives B a start of 16 m and still beats him by 40 s,what will be the speed of B?

Options

A. 6 m/s
B. 8 m/s
C. 15 m/s
D. 5.9 m/s

Answer

To solve the problem, we need to find the speed of B given the conditions of the race between A and B.

### Step-by-Step Solution:

1. **Understanding the Race Conditions**:
- A runs a distance of 400 meters.
- A runs at a speed of 16 m/s.
- B gets a head start of 16 meters, meaning B only needs to run 400 - 16 = 384 meters.
- A beats B by 40 seconds.

2. **Calculate the Time Taken by A**:
- Time = Distance / Speed
- For A, the time taken to complete 400 meters is:
\[ \text{Time taken by A} = \frac{400 \text{ m}}{16 \text{ m/s}} = 25 \text{ seconds} \]

3. **Determine the Time Taken by B**:
- Since A beats B by 40 seconds, this means B takes 40 seconds more than A to finish the race.
- Therefore, the time taken by B is:
\[ \text{Time taken by B} = \text{Time taken by A} + 40 \text{ seconds} = 25 \text{ seconds} + 40 \text{ seconds} = 65 \text{ seconds} \]

4. **Calculate the Speed of B**:
- Now we can find the speed of B using the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
- The distance B runs is 384 meters, and the time taken is 65 seconds:
\[ \text{Speed of B} = \frac{384 \text{ m}}{65 \text{ s}} \approx 5.9 \text{ m/s} \]

### Final Answer:
The speed of B is approximately **5.9 m/s**.

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