we get that for the first part its rate was 90mph
and to find the time we get that
[tex]\begin{gathered} \begin{cases}x+y=2 \\ 90x+60y=160\end{cases}\rightarrow x=2-y\rightarrow \\ 90(2-y)+60y=160\rightarrow180-90y+60y=160\rightarrow-30y=-20 \\ y=\frac{2}{3} \end{gathered}[/tex]
so the last part of the race was 2/3 hours long and the first part was 4/3 hours long
