Answer:
(D = 25t) is the function that models the distance, D, between the ships in terms of the time, t (in hours), elapsed since their departure.
Explanation:
First ship sailed south at a speed of 15 mi/h, let this be = A
Second ship sailed east at a speed of 20 mi/h, let this be = B
Making a sketch of the position of this two ships, we will obtain a right angled triangle.
The distance between the two ships is the hypotenuse of the right angled triangle, let this be = D
From Pythagoras theorem
D² = A² + B²
To find a function that models the distance, D, between the ships in terms of the time, t (in hours), elapsed since their departure.
⇒ D² = (At)² + (Bt)²
D² = (15t)² + (20t)²
D² = 225t² + 400t²
D² = 625t²
D = √625t²
D = 25t
Therefore, (D = 25t) is the function that models the distance, D, between the ships in terms of the time, t (in hours), elapsed since their departure.
