we know Neil drove 60 miles at 45mph, now, how long was that?
since we know is driving 45 miles in 1 hour, how long will it be for 60 miles?
[tex]\bf \begin{array}{ccll}
miles&hours\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
45&1\\
60&h
\end{array}\implies \cfrac{45}{60}=\cfrac{1}{h}\implies h=\cfrac{60\cdot 1}{45}\implies h=\cfrac{4}{3}[/tex]
so it took that long, for 60 miles.
the remainder of the trip took 1½ hrs and it went at 60mph, how many miles is that?
well, we know he can do 60 miles in 1 hour, how many miles will it be in 1½ which is 3/2 anyway?
[tex]\bf \begin{array}{ccll}
miles&hours\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
60&1\\
m&\frac{3}{2}
\end{array}\implies \cfrac{60}{m}=\cfrac{\quad 1\quad }{\frac{3}{2}}\implies \cfrac{60\cdot \frac{3}{2}}{1}=m\implies 90=m[/tex]
so it was 90 miles at 60mph.
so, the whole trip was 60 + 90 miles total, or 150 miles, and it took 4/3 + 3/2 hours
[tex]\bf \stackrel{\textit{average speed}}{\cfrac{60+90}{\frac{4}{3}+\frac{3}{2}}}\cfrac{miles}{hours}\implies \cfrac{150}{\frac{8+9}{6}}\implies \cfrac{150}{\frac{17}{6}}\implies \cfrac{\frac{150}{1}}{\frac{17}{6}}\implies \cfrac{150}{1}\cdot \cfrac{6}{17}
\\\\\\
\cfrac{900}{17}\cfrac{miles}{hours}\quad \approx \quad 52.941176470588\frac{miles}{hour}[/tex]
