Hello
1) Let's call [tex]v_0 = 8~m/h[/tex] the velocity of the motorboat in calm water. When it travels against the current, the relative velocity will be [tex]v_0-v_c[/tex], where [tex]v_c[/tex] is the current velocity. Similarly, when the motorboat travels with the current, its relative velocity will be [tex]v_0+v_c[/tex].
2) Given [tex]v_r= \frac{S}{t} [/tex], where [tex]v_r[/tex] is the relative velocity, when the motorboat travels against the current the time to cover a distance of [tex]S_1=9~m[/tex] is
[tex]t_1= \frac{S_1}{v_0-v_c} [/tex]
Similarly, when the motorboat travels with the current, the time to cover a distance of [tex]S_2=15~m[/tex] is
[tex]t_2=\frac{S_2}{v_0+v_c} [/tex]
3) The problem says that these two times are equal. So we can write:
[tex] \frac{S_1}{v_0-v_c}=\frac{S_2}{v_0+v_c}[/tex]
And we can solve this to find [tex]v_c[/tex], the current rate:
[tex]v_c=v_0 \frac{S_2-S_1}{S_2+S_1} = 8~mph \frac{15~m-9~m}{15~m+9~m}=2 mph [/tex]
