# Math Help - Related Rates Problem.

1. ## Related Rates Problem.

Two straight roads intersect at right angles. At 10:00 a.m. a car passes through the intersection headed due east at 30 miles per hour. At 11:00 a.m. a truck heading due North at 40 miles per hour passes through the intersection. Assume that the two vehicles maintain the given speeds and directions. At what rate are they separating at 1:00 p.m?

I'm having problems setting it up and solving it. Any help would be greatly appreciated.

2. Originally Posted by dassix
Two straight roads intersect at right angles. At 10:00 a.m. a car passes through the intersection headed due east at 30 miles per hour. At 11:00 a.m. a truck heading due North at 40 miles per hour passes through the intersection. Assume that the two vehicles maintain the given speeds and directions. At what rate are they separating at 1:00 p.m?

I'm having problems setting it up and solving it. Any help would be greatly appreciated.
let $x$ = car's distance east of the origin

$y$ = truck's distance north of the origin

$r$ = straight line distance between the car and truck

$x^2 + y^2 = r^2$

take the time derivative, sub in your given/calculated values and determine the value of $\frac{dr}{dt}$