Question

Consider the Mungo River where it is 200

meters wide and has a uniform flow. A small

boat sailing at full speed takes 5 minutes to

cover 100 meters when sailing upstream, but

only 2 minutes when sailing downstream. What

is the shortest time in which the boat can cross

the Mungo to the nearest point on the opposite

bank?

Answer 1

$\begin{cases} 5=\frac{100}{v_b-v_r},\\ 2=\frac{100}{v_b+v_r}; \end{cases}$

$\begin{cases} {v_b-v_r}=20,\\ {v_b+v_r}=50; \end{cases}$

$\begin{cases} v_b=35~\frac{m}{min},\\ {v_r}=15~\frac{m}{min}; \end{cases}$

$t=\frac{200}{\sqrt{v_b^2+v_r^2}}$

$t\approx 5.25 ~min.$