A river that is $200$ m wide is flowing due east with a speed of $3\mathrm{.}00$ m$/$s relative to the earth. A boat travels due north across the river from point A to point B$.$ If the speed of the boat relative to the water is $5\mathrm{.}00$ m$/$s how long does it take the boat to cross the river?

$($a$)25\mathrm{.}0$ s

N

B

$($b$)34\mathrm{.}3$ s

W

$$

$($c$)40\mathrm{.}0$ s

$

$200$

m

$3$

m$/$s

$($d$)50\mathrm{.}0$ s

$$

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