In a race, runner A runs twice as fast as runner B. If A gives B a head start of $200 \text{ m}$, how far from the starting point must the winning post be located so that they reach it at the exact same time (a dead heat)?
Options:
- A: $300 \text{ m}$
- B: $400 \text{ m}$
- C: $500 \text{ m}$
- D: $600 \text{ m}$
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