In a 1 kilometer race, Runner A beats Runner B by 30 seconds and Runner B beats Runner C by 15 seconds. If Runner A beats Runner C by 180 meters, how many seconds does it take Runner A to complete the 1 kilometer race?

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Let's denote the time taken by runner A to complete the 1 km race as **t seconds**.

Based on the given information:
- Runner B takes **(t + 30) seconds** to complete the race
- Runner C takes **(t + 45) seconds** to complete the race (since B beats C by 15 seconds)

We also know that A beats C by **180 meters**. This means when A completes the full 1000 meters, C has only covered **820 meters** (1000 - 180).

When A completes the race in **t seconds**, C has been running for the same amount of time and has covered 820 meters.

To find how much distance C covers in t seconds, we can set up a proportion:
C covers 1000 meters in (t + 45) seconds
Therefore, in t seconds, C covers: **1000 × t/(t + 45) meters**

Since we know this equals 820 meters:
**1000 × t/(t + 45) = 820**

Cross-multiplying:
**1000t = 820(t + 45)**
**1000t = 820t + 36900**
**180t = 36900**
**t = 205 seconds**

Therefore, runner A completes the 1 kilometer race in **205 seconds**.

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