In 1 km race, A beats B by 18 m or 9 s. Find the A's time over the course

Options

A. 391 s
B. 591s
C. 491 s
D. 500 s

Answer

To solve the problem, we need to find the time taken by A to complete a 1 km race, given that A beats B by 18 meters or 9 seconds.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- A completes the 1 km (1000 meters) race.
- When A finishes, B is 18 meters behind, meaning B has only covered 982 meters.
- B takes 9 seconds to cover the remaining 18 meters.

**Hint**: Identify the distances covered by A and B when A finishes the race.

2. **Finding B's Speed**:
- Since B covers 18 meters in 9 seconds, we can calculate B's speed.
- Speed of B = Distance / Time = 18 m / 9 s = 2 m/s.

**Hint**: Use the formula for speed (Speed = Distance / Time) to find B's speed.

3. **Finding the Time Taken by B to Complete 1000 Meters**:
- We know B covers 982 meters when A finishes the race.
- To find out how long it takes B to cover 1000 meters, we first find the time taken to cover 982 meters.
- Time taken by B to cover 982 meters = Distance / Speed = 982 m / 2 m/s = 491 seconds.

**Hint**: Remember that time = distance / speed.

4. **Calculating A's Time**:
- Since B takes 491 seconds to cover 982 meters, we need to add the 9 seconds it takes for B to cover the remaining 18 meters to find A's total time.
- A's time = Time taken by B to cover 982 meters + Time taken by B to cover 18 meters = 491 seconds + 9 seconds = 500 seconds.

**Hint**: Combine the time taken by B to complete the race to find A's time.

5. **Conclusion**:
- A's time to complete the 1 km race is 500 seconds.

### Final Answer:
A's time over the course is **500 seconds**.