If x represents Jane's speed along the summit then her total exploration time is
[tex]\frac{12}{x}+\frac{40}{(x-5)}=2[/tex]Solving the above equation as
[tex]\begin{gathered} \frac{12(x-5)+40x}{(x)(x-5)}=2 \\ \frac{12x-60+40x}{(x)(x-5)}=2 \\ 52x-60=2(x)(x-5) \\ 52x-60=2(x^2-5x) \\ 52x-60=2x^2-10x \\ 2x^2=52x+10x-60 \\ 2x^2=62x-60 \\ x^2-31x+30=0 \\ x^2-30x-1x+30=0 \\ x(x-30)-1(x-30)=0 \\ (x-30)(x-1)=0 \\ x=30\text{ mph,1 mph} \end{gathered}[/tex]Thus, we get Janes's speed as 30 mph.