Time for road walk = x / 6 hrs time for forest walk = distance / speed?(3-x)² + 2² / 2.5 hrs total time = t = {?(3-x)² + 2² / 2.5} + x/6 dt/dx needs to be 0 for minimum t (1/5) 1/?(3-x)² + 2² (-2)(3-x) + (1/6) = 0 -12(3-x) + 5(?(3-x)² + 2²) = 0 -12(3-x) = - 5(?(3-x)² + 2²) squaring 144(3-x)² = 25(3-x)² + 100 (3-x)² = 100/119 3-x = 0.917 or x = 2.0833 miles = 2.08 miles (iii s. F).
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