Question

A car is traveling west at 67 mi./hr and a truck is traveling south at 59 mi./hr. Both are headed for the intersection of the two roads. At what rate are the car and truck approaching each other when the car is 0.2 mi. and the truck is 0.5 mi. from the intersection?

Answer 1

i have a similar problem like that but dont quite get whether dx/dt= 67mi./hr or 59mi./hr

Answer 2

well, usually x is east-west and y is north-south, dontcha think?

and both are negative, since they are approaching (0,0).

dx/dt = -67
dy/dt = -59

The distance z is

z^2 = x^2+y^2
2z dz/dt = 2x dx/dt + 2y dy/dt

now just plug in z at the desired moment, and then the rest of your numbers.