Answer:
[tex]\large\boxed{75=\dfrac{40+1.5s}{2}\to s\approx73\ mph}[/tex]
Step-by-step explanation:
[tex]s=\dfrac{d}{t}\\\\s-speed\\d-distance\\t-time\\\\average\ speed=\dfrac{total\ distance}{total\ time}[/tex]
[tex]\text{We have:}\\\\s_1=80\ mph\\t_1=0.5\ h\\s_2=?\\t_2=2h-0.5h=1.5\ h\\\\d_1=(80)(0.5)=40\ mi\\d_2=s_2(1.5)=1.5s_2\ mi\\\\total\ distance=d_1+d_2=(40+1.5s_2)\ mi\\total\ time=2\ h\\average\ speed=75\ mph\\\\\text{Substitute:}\\\\75=\dfrac{40+1.5s_2}{2}[/tex]
[tex]\text{Solution:}\\\\75=\dfrac{40+1.5s_2}{2}\qquad\text{multiply both sides by 2}\\\\150=40+1.5s_2\qquad\text{subtract 40 from both sides}\\\\110=1.5s_2\qquad\text{divide both sides by 1.5}\\\\\dfrac{110}{1.5}=s_2\to s_2=\dfrac{1100}{15}=\dfrac{220}{3}=73.333...\approx73\ mph[/tex]
