Answer:
In traffic, she drove for 3 hours
and After the traffic cleared she drove for 2 hours.
Explanation:
Given that the road trip was 136 miles;
[tex]d=136[/tex]The first part of the trip there was lots of traffic, she only averaged 16 mph;
[tex]v_1=16[/tex]The second part of the trip there was no traffic so she could drive 44 mph;
[tex]v_2=44[/tex]She traveled for a total of 5 hours;
[tex]t=5[/tex]let x represent the time in traffic when she traveled at 16 mph
[tex]t_1=x[/tex]the time the traffic is clear would be;
[tex]t_2=t-t_1=5-x[/tex]Recall that distance equals speed multiply by time;
[tex]d=v_1t_1_{}_{}^{}+v_2t_2[/tex]substituting the values;
[tex]136=16x+44(5-x)[/tex]solving for x;
[tex]\begin{gathered} 136=16x+220-44x \\ 44x-16x=220-136 \\ 28x=84 \\ x=\frac{84}{28} \\ x=3 \end{gathered}[/tex]So;
[tex]\begin{gathered} t_1=3\text{ hours} \\ t_2=5-x=5-3=2 \\ t_2=2\text{ hours} \end{gathered}[/tex]Therefore, In traffic, she drove for 3 hours
and After the traffic cleared she drove for 2 hours.
