Two racing boats set out from the same dock and speed away at the same constant speed of $116k\frac{m}{h}$ for half an hour $(0\mathrm{.}500h),$ the blue boat headed $24\mathrm{.}6$ south of west, and the green boat headed $40\mathrm{.}1$ south of west. During this half$-$hour $($a$)$ how much farther west does the blue boat travel, compared to the green boat, and $($b$)$ how much farther south does the green boat travel, compared to the blue boat? Express your answers in $km.$

$($a$)$ Number

Units

$($b$)$ Number

Units