A small island is 2 km off shore in a large lake .A woman on the island can row her boat 10 km/hr and can run at a speed of 20 km/hr. If she rows to the closest point of the straight shore, she will land 6 km from a village on the shore. Where should she land to reach the village most quickly by a combination of rowing and running?

Question

Steve · Answer

if she lands a distance x from the closest point on shore, she is 6-x from the village. So, she will

row √(x^2+36) km
run 6-x km

So, her travel time will be

t = √(x^2+36)/10 + (6-x)/20
dt/dx = (2x - √(x^2+36)) / 20√(x^2+36)

Since the denominator is never zero, dt/dx=0 when

2x - √(x^2+36) = 0
x = 2√3

So, she needs to land 2√3 km from the nearest point on shore.

Mark · Answer

row must be sqr rt of (x^2+4); therefore the answer is 2 sqr rt of 3 allover 3 km