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lets see: 13.4 mi/39mi/gal miles cancel and you're left with 0.3436 gallons used.
8.9mi/28mi/gal =0.31785 gallons used. This is only for the two effective alternate routes available after the initial 20 miles as per the problem statement.
It would appear that strictly based on distance you would come ahead even with worse mpg, however in the real world you'd need to factor in the extra time spent idling if you did not shut the engine off at the red lights, this could tip the fuel usage back into the favor of the higher speed/distance of the motor way cruise because of the higher cumulative mpg.
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