2.80: Optimising journey time across a field

The rectangle $ABCDE$ represents a ploughed field where $AB = 300$ m and $AE = 400$ m. Joseph needs to walk from $A$ to $D$ in the least possible time. He can walk at $0.9\text{ ms}^{-1}$ on the ploughed field and at $1.5\text{ ms}^{-1}$ on any part of the path $BCD$ along the edge of the field. He walks from $A$ to $C$ and then from $C$ to $D$. The distance $BC = x$ m.