- #1

Poppynz

- 6

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Im trying to write an equation for the question below. Could someone please point me in the right direction with writing it?

## Homework Statement

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?

## Homework Equations

## The Attempt at a Solution

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 can't seem to get the right answer-

in fact i get imaginary numbers

this is what i did

y=(1/3)*(16+x^2)^(1/2)-(1/5*x)+2

y'= -1/5+1/2*1/3(16+x^2)^(1/2)*2x

y'= -1/5+(2x/(6(16+x^2)^(1/2))

y'=0

1/5=x/(3(16+x^2)^(1/2))

3*(16+x^2)^(1/2)=5*x //square both sides

9*(16+x^2)=5*x^2

144+9x^2-5x^2=0

x= +/- 6i //this is obviously wrong as a person does not travel imaginary distances