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 2 years ago
A sherman is in a rowboat on a lake and 3
km from shore. He wishes to reach a store 2
km down the (straight) shore. He can row at
5 km/h and run at 13 km/h. To what point
downshore should he row to get to the store
as quickly as possible?
It's supposed to be optimization but I'm wondering if I need to use related rates... :/
 2 years ago
A sherman is in a rowboat on a lake and 3 km from shore. He wishes to reach a store 2 km down the (straight) shore. He can row at 5 km/h and run at 13 km/h. To what point downshore should he row to get to the store as quickly as possible? It's supposed to be optimization but I'm wondering if I need to use related rates... :/

This Question is Closed

completeidiot
 2 years ago
Best ResponseYou've already chosen the best response.2did you draw a picture?

completeidiot
 2 years ago
Best ResponseYou've already chosen the best response.2i dont think you need to use related rates for this question

MarcLeclair
 2 years ago
Best ResponseYou've already chosen the best response.0Yup gives me a right angle triangle dw:1354488913281:dw

MarcLeclair
 2 years ago
Best ResponseYou've already chosen the best response.0the store being the point where 5 km/h and 13km/h meet

completeidiot
 2 years ago
Best ResponseYou've already chosen the best response.2you drew it wrong

completeidiot
 2 years ago
Best ResponseYou've already chosen the best response.2you cant use speed as distance values

MarcLeclair
 2 years ago
Best ResponseYou've already chosen the best response.0im just showing the distance where the speed is going. I thought it was normal to do. ( well for me to understand)

completeidiot
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1354489054440:dw

completeidiot
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1354489176738:dw

MarcLeclair
 2 years ago
Best ResponseYou've already chosen the best response.0Oh yeah ended the triangle too late. I need to find the the point where he reaches the shore, But I usually get 2 equations, ( one is my constraint the other is the one I'm trying to maximize/minimize) I can't figure them out here Perimeter, or area, I mean I feel as if I don't have enough variables.

completeidiot
 2 years ago
Best ResponseYou've already chosen the best response.2d/v=t dw:1354489441544:dw first determine the rowing distance \[d_{row}=\sqrt{x^2+9}\] and running distance \[d_{run}=2x\] now calculate total time to travel said distance \[t= d_{row}/v_{row} + d_{run}/v_{run}\] you should get a nice fun equation then solve for x using first derivative then solve for t

MarcLeclair
 2 years ago
Best ResponseYou've already chosen the best response.0Ahhhhhh so its not always with area and peremeter.... stupid me. THanks a lot , I'll try it from there on my own :P Gotta love math

Chlorophyll
 2 years ago
Best ResponseYou've already chosen the best response.1@MarcLeclair Have you found x yet?

MarcLeclair
 2 years ago
Best ResponseYou've already chosen the best response.0No still trying hehe. Taking some time :(

Chlorophyll
 2 years ago
Best ResponseYou've already chosen the best response.1Total time T = run time + row time ( 2 x ) / 13 + √ ( x² + 9 ) / 5 Can you take derivative:

MarcLeclair
 2 years ago
Best ResponseYou've already chosen the best response.0yeah thats what im trying to do right now, I got (13x/13 ^2) +3(1/2( x ^2+9) ^(1/2) (2x) / 9

MarcLeclair
 2 years ago
Best ResponseYou've already chosen the best response.0er I dont mean 3 I mean 5 sorry got confuse in the numbers. so 5(1/2 * and the last one is /15

Chlorophyll
 2 years ago
Best ResponseYou've already chosen the best response.1T' = x / 5√ ( x² + 9 )  1 / 13

MarcLeclair
 2 years ago
Best ResponseYou've already chosen the best response.0Isn't mine right but not simplified?

Chlorophyll
 2 years ago
Best ResponseYou've already chosen the best response.1T' = 0 x / 5√ ( x² + 9 ) = 1 / 13 5√ ( x² + 9 ) = 13x

MarcLeclair
 2 years ago
Best ResponseYou've already chosen the best response.0Yes thank you chlorophyll :) I ll verify if my derivative was right. Thanks a lot for your help

MarcLeclair
 2 years ago
Best ResponseYou've already chosen the best response.0It is pretty complicated, I've got more complicated to do haha. I'm enjoying it O_o

Chlorophyll
 2 years ago
Best ResponseYou've already chosen the best response.113x = 5√ ( x² + 9 ) > 169x² = 25 ( x² + 9) 144x² = 225 x = 15/12

MarcLeclair
 2 years ago
Best ResponseYou've already chosen the best response.0That's what I got too and it is right. You two were life saviour haha

MarcLeclair
 2 years ago
Best ResponseYou've already chosen the best response.0its okay hahahaha, everybody have their strong points, you still helped with calculations :) I'm aweful at making relationships in math :P

Chlorophyll
 2 years ago
Best ResponseYou've already chosen the best response.1Finally, plug x to find the distance, though :) All credit should go to @completeidiot =)
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