Two cars start moving from the same point. One travels south at 32 mi/h and the other travels west at 24 mi/h. At what rate (in mi/h) is the distance between the cars increasing three hours later?

Question

Two cars start moving from the same point. One travels south at 32 mi/h and the other travels west at 24 mi/h. At what rate (in mi/h) is the distance between the cars increasing three hours later?

Answer 1

in 3 hours, one car is 96 miles south

the other is 72 miles west

the distance between them is = sqr(72^2 + 96^2) = sqr(14400) = 120

d^2 = s^2 + w^2

take the derivative with respect to time

2dd' = 2ss' + 2ww'

divide by 2

dd' = ss' + ww'

d=120, s=96 w = 72, s'=32, w'= 24

plug in the values

120d' = 96(32) + 72(24) = 3072 + 1728= 4800

d' = 4800/120 = 40 mi/h = the increasing rate of of the change in distance between the cars in 3 hours

d'= 40 miles per hour