Question

the shoreline of circle lake is a circle with diameter 2 mi.nancy's training routine begins at point e on the eastern shore of the lake.she jogs along the north shore to a point p and then swims the straight line distance,if any point ,from point to point w diametrically opposite.nancy swims at a rate of 2 mi/h and josh 8 mi/h how far should nancy jog in order to complete her training routine?what is the least and greatest amount of time answer?

Answer 1

Label the center of the circle O. Circle O has radius 1.
If angle EOP is θ, then she
jogs a distance of rθ = θ
swims a distance of r sin(π-θ)/2 = r sin(π/2-θ/2) = r cos(θ/2) = cos θ/2
so, since time = distance/speed, her time is
t(θ) = θ/8 + 1/2 cos(θ/2)
To find min/max, set dt/θ = 0 and solve for θ.