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?

Question

Mathematics

Rachael Contreras

29 May, 00:52

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?

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Phoenix Joyce · Answer 1

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