Mathematics

Problem

A right triangle has horizontal leg length

x(t)

meters and vertical leg length

y(t)

meters. Its aspect ratio is

R(t)=\dfrac{y(t)}{x(t)}

. At the instant when

x=4\,\text{m}

y=3\,\text{m}

\dfrac{dx}{dt}=0.6\,\text{m/s}

, and

\dfrac{dy}{dt}=1.2\,\text{m/s}

, compute

\dfrac{dR}{dt}