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 m/n . When ( m / n ) / 3 (m/n)/3 is expressed as a fraction, the result is p / q p/q . What is p q pq ?


The answer is 6.

Micah Gadbois by Micah Gadbois , 15, USA

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2 solutions

Let L L be the longest distance and S S be the shortest distance, then

L = 100 + 300 = 400 L=100+300=400 and S = 200 S=200

The ratio is 400 200 = 2 \dfrac{400}{200}=2 . Dividing the ratio by 3 3 , we get 2 3 \dfrac{2}{3} .

Finally, p q = 2 ( 3 ) = pq=2(3)= 6 \color{#D61F06}\large \boxed{6}

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Micah Gadbois
Jul 17, 2017

The greatest length that James can run to get to the flag is 100+300 = 400 meters. The shortest length that James can run to get to the flag is 300-100 = 200 meters.

400/200 = 2, m/n = 2, m/n/3 = 2/3, p/q = 2/3, pq = 6

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