the answer has to do with relative speeds.
if an object travels at 100 miles going west and another object travels 100 miles per hour going east, then the distance between them will be as if one of the objects was standing still and the other object was traveling at 200 miles per hour.
this concept appears to be what is happening with these ships.
the ships are traveling on parallel courses 800 meters apart.
the blue line ship is traveling at 8 kilometers per hour going west which is the same as 8000 meters per hour.
converting this to minutes, the blue line ship is traveling at 133.33... meters per minute going west.
when the blue line ship first spots the white line ship, they are 1700 meters apart.
this forms a right triangle where the vertical distance is 800 meters and the hypotenuse distance is 1700 meters.
a little trigonometry from pythagorus shows the horizontal distance between them to be 1500 meters.
the blue line ship will keep the white line ship in view until it has past the white line ship and gone another 1500 meters.
this forms an isosceles triangle where the legs of the isosceles triangle are each 1700 meters in length and the base of the isosceles triangle is 3000 meters in length.
this all assumes the white line ship is not moving at all, but is dead in the water.
if that's the case, then it would take the blue line ship 22.5 minutes from the time it first sees he white line ship until the time it last sees the white line ship.
that particular scenario is captured in the following picture.
when the white line ship is standing still, the blue line ship needs to travel 3000 meters from the time it first spots the white line ship until the time it last spots the white line ship.
if the blue line ship is traveling at 133.33... meters per minute, then it takes 22.5 minutes from the time it first sees the white line ship until the time it can't see the white line ship anymore.
this is because rate * time = distance.
when rate is 133.33... meters per minute and distance is 3000 meters, solve for time to get time = 22.5 minutes.
that's too long, so the white line ship can't be standing still.
it has to be moving at some rate of speed going east so that the time they are in sight of each other is only 15 minutes.
assuming the white line ship was still standing still, i then determined how fast the blue line ship needs to be moving in order to only be able to spot the white line ship for 15 minutes.
the same formula was used, i.e. rate * time = distance.
the distance was still 3000 meters because the white line ship was still standing still.
the time was 15 minutes.
i solved for rate to get rate = 200 meters per minute.
when the rate was 200 meters per minute, then rate * time became 200 * 15 = 3000 meters distance.
relative to the white line ship, the blue line ship needed to be moving 200 meters per minute.
the difference between 200 meters per minute and 133.33... meters per minute is 66.66... meters per minute.
i then theorized that, perhaps, if the white line ship was moving at 66.66... meters per minute in the opposite direction of the blue line ship moving at 133.33... meters per minute, then the combined speed would be the same as if the blue line was moving at 200 meters per minute and the line ship was standing still.
i then drew a graph to see if this gave me what i wanted.
in 15 minutes, the blue line ship moved 2000 meters westwards from when it first spotted the white line ship.
during the same 15 minutes, the white line ship moved 1000 meters eastward from when it was first spotted by the blue line ship.
this is captured in the next picture as best i can do it.
rate * time = distance.
at 133.33... meters per minute for 15 minutes, the blue line ship traveled 2000 meters going west.
at 66.66... meters per minute for 15 minutes, the white line ship traveled 1000 meters going east.
to understand this, you need to use relative position.
assume the meter positions become more positive as you go west.
when the ships were first in sight of each other, the blue line ship was at position 0 on its course and the white line ship was at position 1500 on its course.
when the ships were last in sight of each other 15 minutes later, the blue line ship was at position 0 on its course and the white line ship was at position 500 on its course.
the horizontal distance between them was 1500 meters when they first caught sight of each other and 1500 meters when they last caught sight of each other.
when they first caught sight of each other, the blue line ship was east of the white line ship.
when they last caught sight of each other, the blue line ship was west of the white line ship.
the blue line ship was traveling west at 133.33..... meters per minutes which equates to 8000 meters per hour which is the same as 8 kilometers per hour.
the white line ship was traveling east at 66.66... meters per minutes which equates to 4000 meters per hour which is the same as 4 kilometers per hour.
your solution appears to be that the white line ship was traveling at a velocity of 4 kilometers due east.