Chapter $18$: A $3-$in$-$thick slab is $10$ in wide and $15$ ft long. The thickness of the slab is reduced by $20\%$ and width increases by $3\%$ in a hot$-$rolling operation. If the entry speed of the slab is $40f\frac{t}{m}in,$ determine the $($a$)$ length and $($b$)$ exit velocity of the slab.

$[20$ points$]$