we get that
[tex]\begin{gathered} (r-15)t_1=d \\ (r+15)t_2=d \end{gathered}[/tex]where
[tex]t_1=t_2+1[/tex]using these equations we get:
[tex]\begin{gathered} (r-15)\cdot(t_2+1)=(r+15)\cdot t_2 \\ r\cdot t_2+r-15t_2-15=r\cdot t_2+15t_2 \\ r=30t_2+15 \end{gathered}[/tex]replacing d by 360 and r by the equation above we get
[tex]\begin{gathered} (30t_2+15+15)t_2=360 \\ 30t^2_2+30t_2=360\rightarrow t^2_2+t_2=12 \\ t^2_2+t_2-12=0\rightarrow(t_2+4)(t_2-3)=0 \end{gathered}[/tex]as the time can not be negative. We get that the time the airplane spent using the wind is 3 hours. So the rate without the wind is:
[tex]r=30\cdot3+15=105\text{ miles per hour}[/tex]