MathDB

Alison has an analog clock whose hands have the following lengths:

a

inches (the hour hand),

b

inches (the minute hand), and

c

inches (the second hand), with

a < b < c

. The numbers

a

b

, and

c

are consecutive terms of an arithmetic sequence. The tips of the hands travel the following distances during a day:

A

inches (the hour hand),

B

inches (the minute hand), and

C

inches (the second hand). The numbers

A

B

, and

C

(in this order) are consecutive terms of a geometric sequence. What is the value of

\frac{B}{A}

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