# Related rates question pls help

1. Mar 22, 2008

### trey

A sailor in a boat 10 km off a straight coastline wants to reach a point 20km along the coast in the shortest possible time. Toward what point on the shore should he head if he can row at 4 km/h and run at 12 km/h?

i believe this involves optomizeation as well ralated rates but i am unsure as to how to get the equasion to maximize.

x=10km
sailor ---------- | (straight coast)
dx/dt=4 km/h |
| y= 20 km dy/dt= 12 km/h
|
|

2. Mar 22, 2008

### trey

srry guys, i tried to make a picture at the bottom. I didnt know it wouldn't permit the spaces i input.

3. Mar 22, 2008

### arildno

Let x=0 be the point on the coast directly fronting the boat.

Call the unknown point at the coas for X.

Then, the time it takes for him to reach X by the boat is $\frac{\sqrt{10^{2}+X^{2}}}{4}$
and the time for him to reach his destination after that $\frac{20-X} {12}$
Thus, his total time T(X) is given by:
$$T(X) =\frac{\sqrt{10^{2}+X^{2}}}{4}+\frac{20-X} {12}$$
Do you agree with this?