Answer:
18.87 km/hr
Step-by-step explanation:
First boat is heading North with a speed of 10 km/hr.
Second boat is heading West with a speed of 16 km/hr.
Time for which they move = 2.5 hours
To find:
The speed at which the distance is increasing between the two boats.
Solution:
Let the situation be represented by the attached diagram.
Their initial position is represented by point O from where they move towards point A and point B respectively.
[tex]Distance = Speed \times Time[/tex]
[tex]Distance\ OA = 10 \times 2.5 = 25\ km[/tex]
[tex]Distance\ OB = 16 \times 2.5 = 40\ km[/tex]
We can use Pythagorean Theorem to find the distance AB.
AB is the hypotenuse of the right angled [tex]\triangle AOB[/tex].
According to Pythagorean theorem:
[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow AB^{2} = OA^{2} + OB^{2}\\\Rightarrow AB^2 = 25^2 + 40^2\\\Rightarrow AB^2 = 2225^2\\\Rightarrow AB^2 \approx 47.17\ km[/tex]
The speed at which distance is increasing between the two boats is given as:
[tex]\dfrac{47.17}{2.5} \approx 18.87\ km/hr[/tex]
