Posted by Shihara on Thursday, March 15, 2012 at 8:10am.
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?

Math  Steve, Thursday, March 15, 2012 at 2:07pm
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. 
Math  kaycee, Tuesday, May 31, 2016 at 6:36am
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?