A beats B by 125 m in a kilometer race. Find B’s speed if A’s speed is 16 m/sec.:

Options

A. 18 m/sec
B. 14 m/sec
C. 7 m/sec
D. 21 m/sec

Answer

To solve the problem, we need to determine B's speed given that A beats B by 125 meters in a 1-kilometer race and A's speed is 16 m/sec.

### Step-by-Step Solution:

1. **Understand the race distance**: The total distance of the race is 1 kilometer, which is equal to 1000 meters.

2. **Determine the distance covered by B**: Since A beats B by 125 meters, when A finishes the race (1000 meters), B has only covered:
\[ 1000 \text{ meters} - 125 \text{ meters} = 875 \text{ meters} \]

3. **Calculate the time taken by A**: We know A's speed is 16 m/sec. The time taken by A to complete the race can be calculated using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{1000 \text{ meters}}{16 \text{ m/sec}} = 62.5 \text{ seconds} \]

4. **Calculate B's speed**: Now, we need to find B's speed. We know B covers 875 meters in the same time (62.5 seconds) that A takes to cover 1000 meters. B's speed can be calculated as:
\[ \text{Speed of B} = \frac{\text{Distance}}{\text{Time}} = \frac{875 \text{ meters}}{62.5 \text{ seconds}} = 14 \text{ m/sec} \]

5. **Conclusion**: Therefore, B's speed is:
\[ \text{B's speed} = 14 \text{ m/sec} \]

### Final Answer:
B's speed is 14 m/sec.

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