A man in a boat crosses a river from point $A$. If he rows perpendicular to the banks he reaches point $C(BC=120 \mathrm{m})$ in $10 \min$. If the man heads at a certain angle $\alpha$ to the straight line $AB(AB$ is perpendicular to the banks) against the current he reaches point $B$ in $12.5 \min$. 

Find the width of the river $w$, the rowing velocity $u$, the speed of the river current $v$ and the angle $\alpha$. Assume the velocity of the boat relative to water to be constant and the same magnitude in both cases.