Two Boats word problem - need function (please help)

May 2010
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0
A boat leaves a dock at 2:00PM, and travels directly south at a speed of 20 miles per hour. Another boat is traveling towards the dock, from the west at a speed of 15 miles per hour. This boat will arrive at the dock at 3:00pm.


a) write a function for the distance between the two boats in terms of x, where x = the amount of time (in hours) since 2:00pm.


b) At what time were the two boats closest together?




Thank you so much for any help you can give me.
 

skeeter

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Jun 2008
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A boat leaves a dock at 2:00PM, and travels directly south at a speed of 20 miles per hour. Another boat is traveling towards the dock, from the west at a speed of 15 miles per hour. This boat will arrive at the dock at 3:00pm.


a) write a function for the distance between the two boats in terms of x, where x = the amount of time (in hours) since 2:00pm.


b) At what time were the two boats closest together?
using t for time rather than x ...

let the dock location be the origin

position (x,y) of the first boat ... \(\displaystyle (0, -20t)\)

position (x,y) of the second boat ... \(\displaystyle (15t-15, 0)\)

distance formula ...

\(\displaystyle d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

distance between the two boats ...

\(\displaystyle d = \sqrt{(15t-15)^2 + (20t)^2}\)

graph the distance function to find the minimum.
 
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