help question about fractions

The initial rate of the scuba is -8 1/2 feet per minute
The given parameters are:
Final rate = -12 3/4 feet per minute
Final rate = 1 1/2 times the initial rate
This means that:
-12 3/4 feet per minute = 1 1/2 times the initial rate
Rewrite the expression as:
-12 3/4 feet per minute = 1 1/2 * initial rate
Express as improper fractions
-51/4 feet per minute = 3/2 * initial rate
Multiply through by 2/3
Initial rate = -8 1/2 feet per minute
Hence, the initial rate of the scuba is -8 1/2 feet per minute
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