## MarcLeclair Group Title 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 down-shore 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

1. completeidiot Group Title

did you draw a picture?

2. completeidiot Group Title

i dont think you need to use related rates for this question

3. MarcLeclair Group Title

Yup gives me a right angle triangle |dw:1354488913281:dw|

4. MarcLeclair Group Title

the store being the point where 5 km/h and 13km/h meet

5. completeidiot Group Title

you drew it wrong

6. completeidiot Group Title

you cant use speed as distance values

7. MarcLeclair Group Title

im just showing the distance where the speed is going. I thought it was normal to do. ( well for me to understand)

8. completeidiot Group Title

|dw:1354489054440:dw|

9. completeidiot Group Title

|dw:1354489176738:dw|

10. MarcLeclair Group Title

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.

11. completeidiot Group Title

d/v=t |dw:1354489441544:dw| first determine the rowing distance $d_{row}=\sqrt{x^2+9}$ and running distance $d_{run}=2-x$ 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

12. MarcLeclair Group Title

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

13. Chlorophyll Group Title

@MarcLeclair Have you found x yet?

14. MarcLeclair Group Title

No still trying hehe. Taking some time :(

15. Chlorophyll Group Title

Total time T = run time + row time ( 2- x ) / 13 + √ ( x² + 9 ) / 5 Can you take derivative:

16. MarcLeclair Group Title

yeah thats what im trying to do right now, I got (-13x/13 ^2) +3(1/2( x ^2+9) ^(-1/2) (2x) / 9

17. MarcLeclair Group Title

er I dont mean 3 I mean 5 sorry got confuse in the numbers. so 5(1/2 * and the last one is /15

18. Chlorophyll Group Title

T' = x / 5√ ( x² + 9 ) - 1 / 13

19. MarcLeclair Group Title

Isn't mine right but not simplified?

20. Chlorophyll Group Title

T' = 0 x / 5√ ( x² + 9 ) = 1 / 13 5√ ( x² + 9 ) = 13x

21. MarcLeclair Group Title

Yes thank you chlorophyll :) I ll verify if my derivative was right. Thanks a lot for your help

22. MarcLeclair Group Title

It is pretty complicated, I've got more complicated to do haha. I'm enjoying it O_o

23. Chlorophyll Group Title

13x = 5√ ( x² + 9 ) -> 169x² = 25 ( x² + 9) 144x² = 225 x = 15/12

24. MarcLeclair Group Title

That's what I got too and it is right. You two were life saviour haha

25. Chlorophyll Group Title

=> x = 1hr 15'

26. MarcLeclair Group Title

its okay hahahaha, everybody have their strong points, you still helped with calculations :) I'm aweful at making relationships in math :P

27. Chlorophyll Group Title

Finally, plug x to find the distance, though :) All credit should go to @completeidiot =)