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?

1 Answer
Alan P.
Oct 12, 2016

#color(green)(2:06PM)#

Explanation:

Warning: This question was asked under "Law of Cosines". The following does not use the "Law of Cosines"
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Based on the Pythagorean Theorem
the boat must travel #sqrt(24^2-20^2)=sqrt(176)=4sqrt(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"#
#color(white)("XXX")#or
#color(white)("XXX")(60" minutes")/(12" miles")#

Traveling #4sqrt(11)" miles"# will take
#color(white)("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" hour " 6" minutes"# after #1PM# is #2:06PM#

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