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A school collects rainwater in a tank. During a shower, water flows in at the rate r(t) = 6t - t²…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A school collects rainwater in a tank. During a shower, water flows in at the rate $r(t) = 6t - t^2$ litres per minute, where $t$ is the time in minutes since the rain began, for $0 \le t \le 6$ . Find the total volume of water that flows into the tank in the six minutes, and the mean rate of flow over this time.

Need a reminder? The key ideaShow

The mean value of $f$ on $[a, b]$ is $\dfrac{1}{b - a}\displaystyle\int_a^b f(x)\,dx$ . The total change from a rate $r(t)$ is $\displaystyle\int_a^b r(t)\,dt$ . Displacement is $\displaystyle\int v\,dt$ , and distance is $\displaystyle\int |v|\,dt$ , found by splitting at the zeros of $v$ .

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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