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To run to school, Johnny travels m/8 miles, which takes m/8 / (8 m/h) = 1/64 h = 1.5 minutes.
To walk home, Johnny travels m/16 miles, which takes m/16 / (4 m/h) = 1/64 h = 1.5 minutes.
Thus, Johnny takes 1.5 - 1.5 = <<1.5-1.5=0>>0 minutes longer to walk home than to run to school. Answer: \boxed{0}.