Let's first convert all units to the same system, for example, to km/h.
The boat travelling east is going at a speed of 8 km/h.
Let's denote the speed of the boat travelling west as v km/h.
The distance between the two boats is decreasing at a rate of (8 + v) km/h (since they are moving in opposite directions).
We know that at one point, the boat travelling east was 200 m east of the boat travelling west. This is equivalent to a distance of 0.2 km.
After 15 minutes, the visibility is reduced to 5 km. This means that the two boats are now at a distance of 5 km from each other, and they are no longer visible to each other.
Using the formula distance = speed x time, we can write:
0.2 + 15/60(8+v) = 5
Simplifying this equation, we get:
0.2 + (2/3)(8+v) = 5
0.2 + (16/3) + (2/3)v = 5
(2/3)v = 5 - 0.2 - (16/3)
(2/3)v = 2.46666667
v = 3.7 km/h (rounded to one decimal place)
Therefore, the constant speed of the boat travelling west is 3.7 km/h.