A point on an island is located 24miles southwest of a dock. A ship leaves the dock at 1:00pm traveling west at 12 miles per hour. At what time(s) to the nearest minute is the ship 20miles from the point?

Oct 12, 2016

$\textcolor{g r e e n}{2 : 06 P M}$

Explanation:

Warning: This question was asked under "Law of Cosines". The following does not use the "Law of Cosines"
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Based on the Pythagorean Theorem
the boat must travel $\sqrt{{24}^{2} - {20}^{2}} = \sqrt{176} = 4 \sqrt{11}$ miles West
to be $20$ miles North of the "point on the island"

The ratio of distance to time for the boat is
color(white)("XXX")12" miles": 1" hour"=12" miles": 60" minutes"
$\textcolor{w h i t e}{\text{XXX}}$or
$\textcolor{w h i t e}{\text{XXX")(60" minutes")/(12" miles}}$

Traveling $4 \sqrt{11} \text{ miles}$ will take
$\textcolor{w h i t e}{\text{XXX")(4sqrt(11)" miles")/(color(white)("X"))xx(60" minutes")/(12 " miles}}$

color(white)("XXX")=20sqrt(11) " minutes"

color(white)("XXX")=66 " minutes" (using a calculator, the nearest minute)

color(white)("XXX")=1" hour " 6" minutes"

$1 \text{ hour " 6" minutes}$ after $1 P M$ is $2 : 06 P M$