Sheils travels from her house to school 1 (5/8) = (1*8 + 5)/8 = 13/8 miles and the same distance back. The length of her round trip (from her house to school + from school to her house) is 13/8+ 13/8 = 2*(13/8) = 26/8 miles.

Dan travels from his house to school 1 (1/3) = (1*3 + 1)/3 = 4/3 miles and the same distance back. The length of her round trip (from house to school + from school to house) is 4/3 + 4/3 = 2*(4/3) = 8/3 miles.

26/8 - 8/3 = (26*3)/(8*3* - (8*8)/(8*3) = (26*3 - 8*8)/24 = 14/24 = 7/12 miles = 0.583 miles approximately

Sheila's round trip is 0.583 miles approximately longer than Dan's round trip.