Question 575520
Two ships leave port at the same time.
 One sails south at 15 miles per hour and the other sails east at 20 miles per hour.
 Find a function that models the distance between the ships in terms of time elapsed since their departure. 
:
Let t = time from departure
:
We know that d = speed*time, therefore
15t = distance traveled by the southbound ship
20t = distance traveled by the eastbound
:
This is a right triangle problem: c^2 = a^2 + b^2, where
a = 15t
b = 20t
c = distance between them at t time
:
c^2 = (15t)^2 + (20t)^2
c^2 = 225t^2 + 400t^2
Combine like terms
c^2 = 625t^2
Find the square root of both sides
c = {{{sqrt(625t^2)}}}
which is
c = 25t
f(t) = 25t, would be the function