A car leaves Oak Corners at 1130 AM traveling south at 60 mp

A car leaves Oak Corners at 11:30 AM traveling south at 60 mph. At the same time, another car is 50 miles west of Oak Corners traveling east at 40 mph. Express the distance d between the cars as a function of the time t after the first car left Oak Corners.

Solution

It\'s not clear which is the \"1st car\", but starting from the time one car is 50 miles west (1130):
d^2 = (50 - 40t)^2 + (60t)^2
d^2 = 2500 - 4000t + 1600t^2 + 3600t^2
d^2 = 5200t^2 - 4000t + 2500
d(t) = 10sqrt(52t^2 - 40t + 25) t in hours, d in miles