A water trough is $4\ \text{m}$ long. Its two ends are vertical isosceles triangles with the vertex at the bottom, as in the figure: each end is $1.2\ \text{m}$ wide across the top and $0.8\ \text{m}$ deep. A pipe pours water into the trough at $0.15\ \text{m}^3$ per minute, and at the same time a crack along the bottom lets water leak out at $0.03\ \text{m}^3$ per minute. Both rates stay steady. At one moment the water in the trough is $0.4\ \text{m}$ deep. At what rate is the water level rising at that moment? Give the answer in $\text{cm/min}$.

Fig. 1: A sketch of a long water trough 4 m long whose ends are triangles with the vertex at the bottom, each 1.2 m wide at the top and 0.8 m deep. Water fills the lower part to a depth h. An arrow shows water pouring in from a pipe at 0.15 cubic metres per minute, and drops show a leak at the bottom at 0.03 cubic metres per minute.