Question

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?

Answer 1

`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`