Question

Boat A leaves a dock headed due east at 2:00PM traveling at a speed of 9 mi/hr. At the same time, Boat B leaves the same dock traveling due south at a speed of 15 mi/hr. Find an equation that represents the distance d in miles between the boats and any time t in hours.

Answer 1

Answer: $17.5t$

Step-by-step explanation:

Given

Speed of boat A is $v_a=9\ mi/hr$

Speed of boat B is $v_b=15\ mi/hr$

Both are moving perpendicular to each other

Distance traveled by Boat A $x_a=9t$

Distance traveled by Boat B $x_b=15t$

Distance between them is given by Pythagoras theorem

$\Rightarrow d^2=(x_a)^2+(x_b)^2\\\\\Rightarrow d^2=(9t)^2+(15t)^2\\\\\Rightarrow d=\sqrt{(9t)^2+(15t)^2}\\\\\Rightarrow d=\sqrt{81t^2+225t^2}\\\\\Rightarrow d=\sqrt{306t^2}\\\\\Rightarrow d=17.49t\approx 17.5t\ \text{miles}$

Distance between them is $17.5t$