Question

Allison drove home at 66 mph, but her brother Austin, who left at the same time, could drive at only 46 mph. When Allison arrived, Austin still had 60 miles to go. How far did Allison drive?

Answer 1

The distance is given by:

$d=vt$

where v is the velocity and t is the time. We know that the distance travel by Allison is given by:

$66t$

The distance travel by Austin is given by:

$46t+60$

These distances have to be equal then we equate the expressions and solve for t:

$\begin{gathered} 66t=46t+60 \\ 66t-46t=60 \\ 20t=60 \\ t=\frac{60}{20} \\ t=3 \end{gathered}$

Now that we know how much time it takes Allison to travel, we multiply it her velocity to determine the distance she travelled:

$66(3)=198$

Therefore, Allison drove 198 miles.