A river that is $600$ m wide flows due east with a speed of $3\mathrm{.}00$ m$/$s$.$ A woman steers a motorboat across the river with a velocity relative to the water that has magnitude $5\mathrm{.}00$ m$/$s and direction due north. How long does it take the woman to cross the river?

$($a$)120$ s

$($b$)160$ s

$600$ m

VWIE

$($c$)200$ s

$$

$($d$)267$ s

$($e$)800$ s

$($f$)$ none of the above answers