Respuesta :
We can solve this problem by setting up a system of equations.
We let x be the time Maggie traveled when there is traffic and let y be the time Maggie traveled when there is no traffic. The sum of these will be equal to 7 hours, represented in the equation as
[tex]x+y=7[/tex]When we multiply the time and the speed, we get the distance. Since we already defined variables x and y as time, we multiply the speed indicated in the problem with respect to the assigned variables for them. The distance travelled is equal to 209. We have the equation set-up as
[tex]20x+43y=209[/tex]Hence, we have the system of equations written as
[tex]\begin{gathered} x+y=7 \\ 20x+43y=209 \end{gathered}[/tex]We use the elimination method to solve for the value of y. We multiply the first equation by -20. We have
[tex]\begin{gathered} -20x-20y=-140 \\ 20x+43y=209 \end{gathered}[/tex]Solve for y
[tex]\begin{gathered} 23y=69 \\ y=3 \end{gathered}[/tex]Use this value of y to solve the value of x using the first equation. We have
[tex]\begin{gathered} x+3=7 \\ x=7-3 \\ x=4 \end{gathered}[/tex]As we stated above, x represents the time Maggie traveled in traffic while y represents the time Maggie traveled in no traffic.
Therefore, it took Maggie 4 hours to drive while in traffic. Also, she drove for 3 hours after the traffic was cleared.
