4. Two ships leave port at the same time. One sails south at 15 mi/h, and the other sails east at 20 mi/h. Find a function that models the distance, D, between the ships in terms of the time, t (in hours), elapsed since their departure.

(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.

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