Car A is traveling north on Highway 16 and car B is traveling west on Highway 83

Question

Car A is traveling north on Highway 16 and car B is traveling west on Highway 83. Each car is approaching the intersection of these highways. At a certain moment, car A is 88 km from the intersection and traveling at 75 km/h while car B is 66 km from the intersection and traveling at 55 km/h. How fast is the distance between the cars changing at that moment? I'm not following on the other explanations posted. I think the others are missing crucial steps that are keeping me from understanding the steps involved.

Explanation / Answer

Let s be the distance between two cars

s = sqrt(x^2 + y^2)

ds/dt = (xdx/dt + ydy/dt ) / sqrt(x^2 + y^2)

= 88*75 + 66*55 / sqrt(88^2 + 66^2) = 93km/h

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