The Golden Flag

Geometry Level pending

James sees a Golden Flag swaying in the wind. Suddenly, a strong gust of wind blows the flag off. James is 100 meters from the flag pole, the flag is carried to a place 300 meters from the flag pole. The ratio of the longest distance James has to run to the shortest distance James has to run to get the flag can be expressed has $$m/n$$. When $$(m/n)/3$$ is expressed as a fraction, the result is $$p/q$$. What is $$pq$$?

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