Thread: Two Boats word problem - need function (please help)

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.

Originally Posted by Cwhitten85

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 ...

position (x,y) of the second boat ...

distance formula ...



distance between the two boats ...



graph the distance function to find the minimum.