Allison drove home at 65 mph, but her brother Austin, who left at the same time, could drive at only 41 mph. When Allison arrived, Austin still had 144 miles to go. How far did Allison drive?

If the distance is x miles, the time Allison drove is x/65.

So, since distance = speed * time,
x = (x/65)(41) + 144

To find the distance that Allison drove, we can start by determining the time it took for her to reach her destination. We know that she drove at 65 mph, and the time it took can be represented by the variable "t." Thus, the equation for Allison's distance is:

Distance = Speed × Time

Let's use this equation to determine the time it took Allison to reach her destination:

Distance = 65 mph × t hours

For Austin, we are given that when Allison arrived, he still had 144 miles to go. Since his speed is 41 mph, we can find the time it took him to travel this distance using the same equation:

144 miles = 41 mph × t hours

Now we have two equations with two variables (the distances and the times):

Distance_Allison = 65 mph × t hours

144 miles = 41 mph × t hours

To solve this system of equations, we can isolate "t" in the second equation and substitute it into the first equation:

t = 144 miles / 41 mph

t ≈ 3.512 hours

Now that we have the time it took for Allison to reach her destination, we can find the distance she drove:

Distance_Allison = 65 mph × 3.512 hours

Distance_Allison ≈ 227.18 miles

Therefore, Allison drove approximately 227.18 miles.