Posted by **erica** on Sunday, October 7, 2012 at 11:57pm.

A car is traveling north towards an intersection at 60mph at the same time a truck is headed east toward the same intersection at 45mph. Find the rate of change of the distance between the car and truck when the car is 3 miles south of the intersection and the truck is 4 miles west of the intersection. Is this distance increasing or decreasing at that time?

- FREE BODY DIAGRAM calculus -
**Reiny**, Monday, October 8, 2012 at 8:34am
Place the car on the negative y axis and label the distance to the origin y

Place the truck on the negative x axis and label the distance to the origin x

label the distance between them d

then

d^2 = x^2 + y^2

2d dd/dt = 2x dx/dt + 2y dy/dt

dd/dt =(x dx/dt + y dy/dt)/d

Given: when x = 4 , dx/dt = -45

when y = 3 , dy/dt = -60

d = 5 , (did you notice the 3-4-5 right-angled triangle ?)

dd/dt = (4(-45) + 3(-60)/5 = -72

At that moment the distance between them is **decreasing** at 72 mph

The distance between them is decreasing, since dd/dt is negative.

- FREE BODY DIAGRAM calculus -
**fikralem**, Tuesday, March 11, 2014 at 12:46pm
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