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Two boats are travelling away from each other in opposite directions. One boat is travelling east at the constant speed of 8 km/h and the other boat is travelling west at a different constant speed. At one point, the boat travelling east was 200 m east of the boat travelling west, but 15 minutes later they lose sight of each other. If the visibility at sea that day was 5 km, determine the constant speed of the boat travelling west

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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.
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