Total distance = 277 miles
Rate of first part trip = 54 miles per hour
Rate of the second part trip = 56 miles per hour
Total time = 5 hours
let
t = travel time of first part
5 - t = travel time of second part
Therefore,
[tex]\begin{gathered} speed=\frac{dis\tan ce}{\text{time}} \\ \text{distance}=\text{speed}\times time \end{gathered}[/tex]First part distance
[tex]\text{distance}=54t[/tex]Second part distance
[tex]\begin{gathered} \text{distance}=56(5-t) \\ \text{distance}=280-56t \end{gathered}[/tex]Total distance equation
[tex]\begin{gathered} 277=54t+(280-56t) \\ 277=54t+280-56t \\ 277-280=54t-56t \\ -3=-2t \\ t=\frac{-3}{-2}=\frac{3}{2}=1.5\text{ hours} \end{gathered}[/tex]Travel time of first part trip = 1.5 hours
Travel time of second part trip = 5 - 1.5 = 3.5 hours
