Water flows into an empty tank at the rate r(t) = 12 - 2t litres per minute for 0 ≤ t ≤ 6, where t…

Water flows into an empty tank at the rate $r(t) = 12 - 2t$ litres per minute for $0 \le t \le 6$, where $t$ is the time in minutes. The pump slows down steadily, and at $t = 6\ \text{min}$ the rate is zero and the pump stops. A computer keeps a log of the flow. The volume $V(t)$ in litres of water in the tank at time $t$ is the area under the rate graph from $0$ to $t$. This is the area function, so $V'(t) = r(t)$ and $V(0) = 0\ \text{L}$. A technician wants three numbers. First, the total volume that enters the tank by the time the pump stops. Second, the time at which the tank holds exactly $20\ \text{L}$. Third, the volume in the tank at $t = 3\ \text{min}$, which is the time when the rate has fallen to half of its starting value. Give the volumes in litres and the time in minutes.