Answer:
The Time taken for David and Amy to be exactly 23 miles apart is 1.014 Hours.
Step-by-step explanation:
Let [tex]t[/tex] be the time taken to reach 23 miles apart from a single point.
David and Amy start at same point and move towards different directions, making them move at perpendicular to each other.
According to pythagoras theorem, and distance = Speed x time.
[tex](17t)^2 + (15t)^2 = 23^2[/tex]
[tex]289t^2 + 225t^2 = 529[/tex]
[tex]\therefore 514t^2 = 529[/tex]
[tex]t^2 = \frac{529}{514}[/tex]
[tex]t^2 = 1.029[/tex]
[tex]\therefore t = \sqrt{1.029} = 1.014 \text{ hours}[/tex]
