t the woman row part way at an angle Θ to the diameter,
and walk along the arc for the rest of the way.
since the triangle on the diameter is right angled, angle subtended at the centre by the arc walked will be 2Θ
distance rowed is 2rcosΘ = 4cosΘ
and length of the arc jogged = r•2Θ = 4Θ, Θ in radians,
so T(Θ) = 4cosΘ/5 + 4Θ/10
= 0.8cosΘ + 0.4Θ
T'(Θ) = -0.8sinΘ + 0.4
but T"(Θ) = -0.8cosΘ, so setting T'(Θ) to 0 will give a MAXIMA
so minimum time has to be at one of the 2 extrema (Θ=0 or pi/2)
T(0) = 0.8
T(pi/2) = 0.4pi/2, < T(0)
so least time = 0.4pi/2 hrs
