# Thread: related rates with cars

1. ## related rates with cars

One car is 3 miles east of an intersection, and it is traveling west at 80 mph. A second car on a crossroad is 4 miles north of the intersection, and is traveling north at 50 mph. Is the the distance between cars increasing or decreasing at the moment, and at what rate. (the distance is decreasing at a rate of 8 mph).

really need help on this problem.

2. Originally Posted by hotdogking
One car is 3 miles east of an intersection, and it is traveling west at 80 mph. A second car on a crossroad is 4 miles north of the intersection, and is traveling north at 50 mph. Is the the distance between cars increasing or decreasing at the moment, and at what rate. (the distance is decreasing at a rate of 8 mph).

really need help on this problem.
let $x$ = distance the west bound car is from the intersection

$\frac{dx}{dt} = -80$ mph (why is this value < 0 ?)

$y$ = distance the northbound car is from the intersection

$\frac{dy}{dt} = 50$ mph

$z$ = straight-line distance between the two cars

$x^2 + y^2 = z^2$

take the time derivative, sub in values ... calculate the value of $\frac{dz}{dt}$