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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... :/
 one year ago
 one year 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... :/
 one year ago
 one year ago

This Question is Closed

completeidiotBest ResponseYou've already chosen the best response.2
did you draw a picture?
 one year ago

completeidiotBest ResponseYou've already chosen the best response.2
i dont think you need to use related rates for this question
 one year ago

MarcLeclairBest ResponseYou've already chosen the best response.0
Yup gives me a right angle triangle dw:1354488913281:dw
 one year ago

MarcLeclairBest ResponseYou've already chosen the best response.0
the store being the point where 5 km/h and 13km/h meet
 one year ago

completeidiotBest ResponseYou've already chosen the best response.2
you drew it wrong
 one year ago

completeidiotBest ResponseYou've already chosen the best response.2
you cant use speed as distance values
 one year ago

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

completeidiotBest ResponseYou've already chosen the best response.2
dw:1354489054440:dw
 one year ago

completeidiotBest ResponseYou've already chosen the best response.2
dw:1354489176738:dw
 one year ago

MarcLeclairBest ResponseYou've already chosen the best response.0
Oh 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.
 one year ago

completeidiotBest ResponseYou've already chosen the best response.2
d/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
 one year ago

MarcLeclairBest ResponseYou've already chosen the best response.0
Ahhhhhh 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
 one year ago

ChlorophyllBest ResponseYou've already chosen the best response.1
@MarcLeclair Have you found x yet?
 one year ago

MarcLeclairBest ResponseYou've already chosen the best response.0
No still trying hehe. Taking some time :(
 one year ago

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

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

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

ChlorophyllBest ResponseYou've already chosen the best response.1
T' = x / 5√ ( x² + 9 )  1 / 13
 one year ago

MarcLeclairBest ResponseYou've already chosen the best response.0
Isn't mine right but not simplified?
 one year ago

ChlorophyllBest ResponseYou've already chosen the best response.1
T' = 0 x / 5√ ( x² + 9 ) = 1 / 13 5√ ( x² + 9 ) = 13x
 one year ago

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

MarcLeclairBest ResponseYou've already chosen the best response.0
It is pretty complicated, I've got more complicated to do haha. I'm enjoying it O_o
 one year ago

ChlorophyllBest ResponseYou've already chosen the best response.1
13x = 5√ ( x² + 9 ) > 169x² = 25 ( x² + 9) 144x² = 225 x = 15/12
 one year ago

MarcLeclairBest ResponseYou've already chosen the best response.0
That's what I got too and it is right. You two were life saviour haha
 one year ago

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

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