4.6 worksheet 2

Math 1300 4.6 Rates and Related Rates (part 2) Name: Solutions3. A car is traveling north toward an intersection at a rate of 60 mph while a truck is travelingeast away from the intersection at a rate of 50 mph. Find the rate of change of the distancebetween the car and truck when the car is 3 miles south of the intersection and the truck is4 miles east of the intersection.xtruck →y↑carzdxdt= 50 miles/hrdydt= −60 miles/hrx 2 + y 2 = z 2When x = 4 and y = 3, we have z = √ 9 + 16 = 5 miles.Differentiating the equation above gives2x dx dy dz+ 2y = 2zdt dt dtdzdt = x dxdt + y dydtz=(4 mi)(50 mi/hr) + (3 mi)(−60 mi/hr)5 mi= 4 miles/hr.The distance between them is increasing at 4 miles/hr.