Please reason step by step, and put your final answer within \boxed{}.
Jack bought an ice cream cone before jogging to the beach. The ice cream cone will normally melt in 10 minutes. However, the weather conditions are affecting the melting rate of the ice cream: there's a 15mph wind blowing in the opposite direction of Jack's running path, and the temperature is 85°F, causing the ice cream to melt 25% faster than in normal conditions. The beach is 16 blocks away, and each block is 1/8th of a mile. How fast does Jack need to jog (in miles per hour) to get to the beach before the ice cream melts, considering the wind and temperature factors?
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