2 cars start at the same location and at the same time Car A travels N at 8mph and car B travels E at 6mph Find the speed at which the distance between the 2 cars is increasing 2 hours after the start

Answer 1

d^2 = n^2 + e^2

take the derivative with respect to time

d= distance between the 2 cars after 2 hours d=sqr((2(8))^2 + ((2)(6))^2) = 10

e = car B's distance from the origin after 2 hours = 2(6) =12

n = car A's distance from the origin after 2 hours = 2(8)=16

2dd' = 2nn' + 2ee'

dd'= nn' + ee'

d' = (nn' + ee')/d= (16(8) + 12(6)/10 = (128+72)/10 = 200/10 = 20 mph

d'=20 mph = rate of change of distance between A and B