Mathematics 9709 · AS & A Level · Differential equations
Differential equations — practice question
A water tank has the form of a cuboid with base area $40000\,\text{cm}^2$. When the time is $t$ minutes, the water depth in the tank is $h$ cm. Water is pumped into the tank at a rate of $50000\,\text{cm}^3$ per minute. Water leaks from the tank through a hole in the bottom at a rate of $600h\,\text{cm}^3$ per minute.
(a)[3]
Show that the relationship $200\,\frac{dh}{dt} = 250 - 3h$ is satisfied.
(b)[5]
Given that $t = 0$ when $h = 50$, find how long it takes for the water depth in the tank to rise to $80\,\text{cm}$. Give your answer correct to $2$ significant figures.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State that $\dfrac{dV}{dt}=50000-600h$.” …