Car A is traveling west at 60 mi/h and car B is traveling north at 40 mi/h. Both are headed for the intersection of the two roads. At what rate are the cars approaching each other when car A is 0.4 mi and car B is 0.3 mi from the intersection?

Let the car A be at distance x and car B be at distance - y from origin (00) Distance between them be r so that, r = √ (.4² +.3²) =.5 mi

r² = x² + y²

differentiating on both sides

2r dr/dt = 2 x dx/dt + 2 ydy / dt

r dr/dt = x dx/dt + ydy / dt

r dr / dt =.4 x 60 +.3 x 40

.5dr / dt =.4 x 60 +.3 x 40

dr / dt = (24 + 12) /.5

= 72 mi / h