related rates question

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bcddd214

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A man is in a boat 2 miles from the nearest point on the coast. His cottage is 3 miles down the coast and 0.5 mile in land. He can row at 2 miles per hour and walk at 4 miles per hour. Where should his boat come in so that he can reach his cottage in the least amount of time?

v_row=2m/h
v_walk=4m/h
v=d/t
t=d/v

there are two relation triangles I am sure, once again I draw a blank in the setup :(
 
Don't draw a blank. That is unlikely to be useful. Draw a lake, a boat, and a cabin. Pick a spot on the shore, between the boat and the cabin. Start drawing right traingles.
 
tkhunny said:
Don't draw a blank. That is unlikely to be useful. Draw a lake, a boat, and a cabin. Pick a spot on the shore, between the boat and the cabin. Start drawing right traingles.
Click to expand...

I have that. I should have stated so before.
Common sense says that the less time rowing and the more time walk would be the solution (or best one)

How to even begin to find the relational has me groveling for mathematical mercy right now.
 
You should have four cardinal components.

1) Horizontal from boat to shore - intersect shore at point P
2) Vertical (down) from P to boat landing - call this point L
3) Horizontal from Cabin to shoreline - call this point C
4) Vertical (up) from C to L

Label the known distances. If it's chopped up, something like 'x' for one and '3-x' for the other might be appropriate.
Calculate the oblique sides of the two right triangles.

Let's see how far you get.
 
You're just writing stuff down. This is no good. Define your terms. What are you talking about? What do the expressions mean?
 
bcddd214 said:
A man is in a boat 2 miles from the nearest point on the coast. His cottage is 3 miles down the coast and 0.5 mile in land. He can row at 2 miles per hour and walk at 4 miles per hour. Where should his boat come in so that he can reach his cottage in the least amount of time?
:(
Click to expand...

Code: 
                      C
                    /|  
                 /   |
              /      |
--P---------*-------P'------
  |      /L
  I    /
  | /
  B

Assume that PLP' is the shoreline. B is the current location of the boat and C is the location of the cabin. Given BP = 2, PP'=3 and CP' = 0.5 Assume that the boat lands at L. So the distance rowed = BL and distance walked = LP'. You want to minimize the time taken to total travel.

Now continue......
 
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