Question

A truck driver drove 80 miles per hour for the first 30 minutes of a 2-hour trip. His average (mean) speed for the entire trip was 75 miles per hour. Which equation can be used to determine his speed, s, for the remaining part of the trip? Select one: a. b. c. d.

Answer 1

`\large\boxed{75=(40+1.5s)/(2)\to s\approx73\ mph}`

Explanation:

`s=(d)/(t)\\\\s-speed\\d-distance\\t-time\\\\average\ speed=(total\ distance)/(total\ time)`

`\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=(40+1.5s_2)/(2)`

`\text{Solution:}\\\\75=(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}\\\\(110)/(1.5)=s_2\to s_2=(1100)/(15)=(220)/(3)=73.333...\approx73\ mph`