Asked by Shihara

A LIGHTHOUSE IS 10 MILES NORTHEAST OF A DOCK. A SHIP LEAVES THE DOCK AT NOON,AND SAILS EAST AT A SPEED OF 12 MILES AN HOUR. AT WHAT TIME WILL IT BE 8 MILES FROM THE LIGHTHOUSE?
Answered by Steve
since the lighthouse is 10 mi NE of the dock, it is 7.07mi east and 7.07 mi north. (legs of a 45-45-90 triangle)

Now, if the ship is 8 mi from the lighthouse, we have a new x-7.07-8 triangle, so x = 3.74.

Now, the distance from the dock to the ship is 7.07 - 3.74 = 3.33 mi.

At 12 mi/hr, that would take 3.33/12 = .277777 hours, or 16'40"

So, at 12:16:40 the ship is 8 mi from the lighthouse

Note: the ship will also be 8 miles from the lighthouse after it has passed it and is east of the lighthouse. From the above data, you can figure the second time with no trouble.
Answered by kaycee
A lighthouse is 15 units of length northwest of a dock. A ship leaves the dock at 8:00 am and travels west at 12 units of length per hour. At what time will the ship be 12 units of length from the lighthouse for the first time?
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