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?

2. 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 ... $(0, -20t)$

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

distance formula ...

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

distance between the two boats ...

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

graph the distance function to find the minimum.