AC is a semicircle and ABCD is a square. Alex and Brian each began at

Hi All,

In these types of situation, you can either approach the work with abstract Algebra and Geometry or you can TEST VALUES and use real values to solve some simple calculations.

IF...
The side of the square = 2 miles
The diameter of the circle = 2 miles
The radius of the circle = 1 mile

Alex travels the semi-circle = (1/2)(Circumference) = (1/2)(2)(pi)(1) = pi miles
Brian travels the 3 sides of the square = 3(2) = 6 miles

We're told that they both traveled for the same amount of TIME, so each of their rates are relative to the distance that they each traveled.

(pi miles)/(6 miles) = ratio of Alex's rate to ratio of Brian's rate = pi/6

Final Answer:

GMAT assassins aren't born, they're made,
Rich

VERITAS PREP OFFICIAL SOLUTION:

Since the diameter of the semicircle is one side of the square, you can start by assigning a variable (say, x) to the diameter. That means that Brian travels 3x as his distance, and for Alex you'll calculate half of the circumference of such a circle: 1/2*xπ. And since the times are the same, the ratio of the rates will be the same as the ratio of the distances. Alex traveled 1/2*xπ while Brian traveled 3x, so the x terms cancel and the ratio is π/2:3 which simplifies to π:6 making A the correct answer.

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