Exercise · ZW-RELATED-RATES-010 · ★★☆ Intermediate

One car is \(3\) km east of an intersection and another is \(4\) km north. The first moves away at \(2\) km/h and the second at \(3\) km/h. How fast is the distance between them changing? (in km/h)

Choose one option.

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  • D. \(\frac{18}{5}\)

Explanation

With \(z^{2}=x^{2}+y^{2}\) we get \(z\,z'=x\,x'+y\,y'\); with \(z=5\), \(z'=\dfrac{3(2)+4(3)}{5}=\dfrac{18}{5}\) km/h.

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Review the concept: Related rates

In a related rates problem several quantities change with time \(t\) and are linked by an equation. The equation is differentiated with respect to \(t\) (chain rule) and the known values are substituted.

\[A=\pi r^{2}\ \Rightarrow\ \frac{dA}{dt}=2\pi r\,\frac{dr}{dt}\]

More practice problems: related rates

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