A, B, C are runing 1 KM race, B beats C by 20 metres or 5 seconds. C beat A by 10 second, what is the speed of A?

Let's break down the problem to find the speed of A.

### Step 1: Analyze the given information.

1. **B beats C by 20 meters or 5 seconds**:
   - This means that when B finishes the 1 km race, C is 20 meters behind.
   - Therefore, the time difference between B and C is 5 seconds.

2. **C beats A by 10 seconds**:
   - This means when C finishes the race, A is 10 seconds behind.

### Step 2: Calculate the speed of B and C.

Since B beats C by 5 seconds and the difference in distance is 20 meters, we can calculate the speed of C.

- The speed of C, \( v_C \), can be calculated using the distance \( d = 20 \) meters and the time difference \( t = 5 \) seconds:

\[
v_C = \frac{20 \text{ meters}}{5 \text{ seconds}} = 4 \text{ meters/second}
\]

### Step 3: Determine the time taken by B to complete the race.

Let's assume B takes \( t_B \) seconds to complete the race.

Since C is 20 meters behind B and their speed difference gives us a time difference of 5 seconds:

\[
t_C = t_B + 5 \text{ seconds}
\]

### Step 4: Calculate the time taken by C to complete the race.

Since C’s speed is \( v_C = 4 \text{ meters/second} \), and the total race distance is 1000 meters:

\[
t_C = \frac{1000 \text{ meters}}{v_C} = \frac{1000}{4} = 250 \text{ seconds}
\]

### Step 5: Find the time taken by A and its speed.

Since C beats A by 10 seconds, the time taken by A, \( t_A \), is:

\[
t_A = t_C + 10 = 250 + 10 = 260 \text{ seconds}
\]

Now, the speed of A, \( v_A \), can be calculated as:

\[
v_A = \frac{1000 \text{ meters}}{t_A} = \frac{1000 \text{ meters}}{260 \text{ seconds}} \approx 3.85 \text{ meters/second}
\]

### Final Answer:
The speed of A is approximately **3.85 meters per second**.

Would you like more details or have any questions? Here are some related questions:

1. How would the speeds of B and C affect the race if they were different?
2. What would be A’s time if the race distance was doubled?
3. How does the time difference affect the outcome of such a race?
4. Can we calculate the speed of B given more information?
5. How does running strategy impact the performance in a race?

**Tip:** When dealing with speed and time problems, always keep track of units and relationships between different runners to avoid confusion.

Learn how to calculate the speed of runner A in a 1 KM race using distance, time, and speed calculations. Detailed step-by-step solution provided with mathematical formulas and logical deductions.

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