Two variables $u$ and $v$ are connected by the equation $\frac{1}{u}+\frac{1}{v}=\frac{1}{20}$

Question

Two variables $u$ and $v$ are connected by the equation $\frac{1}{u}+\frac{1}{v}=\frac{1}{20}$. Given that $u$ and $v$ both vary with time $t$, find an equation connecting $\frac{\mathrm{d}u}{\mathrm{d}t}$, $\frac{\mathrm{d}v}{\mathrm{d}t}$, $u$ and $v$. Given also that $u$ is decreasing at a rate of $2$ units per second, calculate the rate of increase of $v$ when $u=60$ units.[4]

Accepted Answer

$\frac{\mathrm{d}v}{\mathrm{d}t}=-\left(\frac vu\right)^2\frac{\mathrm{d}u}{\mathrm{d}t}$; when $u=60$, $v$ increases at $\frac12\text{ units s}^{-1}$

2019 RI P1 Q2

2019 RI P1 Q2

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