In 100 m race ,A runs at 8 km/h. If A gives B a start of 4 m and still beats him by 15 s,then what is the speed of B (m/s) ?

Options

A. (1) 1.4
B. (2) 2.2
C. (3) 1.6
D. (4) 2.5

Answer

To solve the problem step by step, let's break it down:

### Step 1: Convert A's speed from km/h to m/s
A's speed is given as 8 km/h. To convert this to meters per second (m/s), we use the conversion factor:
\[ \text{Speed in m/s} = \frac{\text{Speed in km/h} \times 1000}{3600} \]
So,
\[ \text{Speed of A} = \frac{8 \times 1000}{3600} = \frac{8000}{3600} = \frac{20}{9} \approx 2.22 \text{ m/s} \]

### Step 2: Calculate the time taken by A to finish the race
The distance of the race is 100 meters. The time taken by A can be calculated using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
Thus,
\[ \text{Time taken by A} = \frac{100}{\frac{20}{9}} = 100 \times \frac{9}{20} = 45 \text{ seconds} \]

### Step 3: Determine the time taken by B
According to the problem, A beats B by 15 seconds. Therefore, the time taken by B is:
\[ \text{Time taken by B} = \text{Time taken by A} + 15 = 45 + 15 = 60 \text{ seconds} \]

### Step 4: Calculate the distance covered by B
Since A gives B a start of 4 meters, B runs a distance of:
\[ \text{Distance covered by B} = 100 - 4 = 96 \text{ meters} \]

### Step 5: Calculate the speed of B
Now, we can find the speed of B using the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
Thus,
\[ \text{Speed of B} = \frac{96}{60} = 1.6 \text{ m/s} \]

### Final Answer
The speed of B is **1.6 m/s**.

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