Given the function of the height of the Elevator A:
[tex]A(t)=80-4t[/tex]And the function of the height of Elevator B:
[tex]B(t)=5.2t+20[/tex]You need to make:
[tex]\begin{gathered} A(t)=45 \\ B(t)=45 \end{gathered}[/tex]Substitute those values into the corresponding function and then solve for "t", in order to find when each elevator is at a height of 45 meters above the ground:
- For Elevator A, you get:
[tex]45=80-4t[/tex][tex]\begin{gathered} 45-80=-4t \\ \\ \frac{-35}{-4}=t \\ \\ t=8.75 \end{gathered}[/tex]- For Elevator B:
[tex]45=5.2t+20[/tex][tex]\begin{gathered} 45-20=5.2t \\ \\ \frac{25}{5.2}=t \\ \\ t\approx4.81 \end{gathered}[/tex]Hence, the answer is:
- For Elevator A:
[tex]t=8.75[/tex]- For Elevator B:
[tex]t\approx4.81[/tex]