A swimmer crosses a flowing stream of width 'w' to and fro in time $t_1$. The time taken to cross the same distance up and down the stream in $t_2.$ If $t_3$ is the time the swimmer would take to swim a distance $2w$ in still water. Then

Question

$$(a)\;{t_1}^2 =t_2t_3\quad (b)\;{t_2}^2=t_1t_3 \quad (c)\;{t_3}^2=t_1t_2 \quad (d)\;t_3=t_1+t_2$$