Math
posted 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?

since the lighthouse is 10 mi NE of the dock, it is 7.07mi east and 7.07 mi north. (legs of a 454590 triangle)
Now, if the ship is 8 mi from the lighthouse, we have a new x7.078 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. 
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?