Im trying to write an equation for the question below. Could someone please point me in the right direction with writing it?
An island is 4km from the nearest point p on the straight shoreline of a lake. if a person can row a boat at 3km/h and walk at 5km/h where should the boat be landed to arrive at a town 10km away is the least time?
I think the equation is y=(1/3)*(4^2+x^2)^(1/2)+((10-x)/5)
this doesn't look hard to differentiate but i cant seem to get the right answer-
in fact i get imaginary numbers
this is what i did
3*(16+x^2)^(1/2)=5*x //square both sides
x= +/- 6i //this is obviously wrong as a person does not travel imaginary distances
Any help would be appreciated