To find the total length of the fence needed for the track, first calculate the length of the rectangular part. If the width of the rectangle is 32' (the diameter of the semi-circles), then the length is 45'. The perimeter of the rectangle is (2 \times (45 + 32) = 154) feet. The two semi-circles together form a full circle with a diameter of 32', giving a circumference of ( \pi \times 32 \approx 100.53) feet. Therefore, the total length of the fence needed is approximately (154 + 100.53 \approx 254.53) feet.
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