An athletic field is a 56 yd​-by-112 yd ​rectangle, with a semicircle at each of the short sides. A running track 10 yd wide surrounds the field. If the track is divided into eight lanes of equal​ width, with lane 1 being the​ inner-most and lane 8 being the​ outer-most lane, what is the distance around the track along the inside edge of each​ lane?

The question is about perimeters at inner dimensions of the  lanes.
Perimeter = 2*longer dimension+ pi*shorter dimensions
Distance between lanes = 10/8 = 1.25 yards (Note: every movement outwards increases the shorter distance by twice this spacing dimension).

Therefore, along the inside edge of each lane, the perimeters are as computed below:

Lane 1: 2*112 + pi*56 = 399.93 yards
Lane 2: 2*112 + pi*(56+2*1.25) = 407.78 yards
Lane 3: 2*112 + pi*(56+4*1.25) = 415.64 yards
Lane 4: 2*112 + pi*(56+6*1.25) = 423.49 yards
Lane 5: 2*112 + pi*(56+8*1.25) = 431. 35 yards
Lane 6: 2*112 + pi*(56+10*1.25) = 439.20 yards
Lane 7: 2*112 + pi*(56+12*1.25) = 447.05 yards
Lane 8: 2*112 + pi*(56+14*1.25) = 454.91 yards