Johnny's home is m miles from school. Johnny runs to school at a speed of 8 mph and then walks home from school at half that speed. How many hours longer does it take Johnny to walk home than to run to school?
The distance from Johnny's home to school is m miles.
To run to school, Johnny travels at a speed of 8 mph, so it takes him (m/8) hours to run to school.
To walk home, Johnny travels at half that speed, or 8 / 2 = <<8/2=4>>4 mph.
Thus, it takes Johnny (m/4) hours to walk home from school.
Therefore, Johnny takes (m/4) - (m/8) = (2m - m)/8 = m/8 hours longer to walk home than to run to school. Answer: \boxed{\frac{m}{8}}.