Allison drove home at 68 mph but her brother who left at the same time could only drive at 54 mph. When Allison arived, her brother still had 84 miles to go. How far did Allison drive?

To find out how far Allison drove, we need to determine the time it took for her to reach home and then use that time along with her speed to calculate the distance. Let's start by finding the time it took for Allison to reach home.

We can use the formula: time = distance / speed

Let's assume the distance Allison drove is D miles. The time it took for Allison to reach home can be calculated as follows:

Time taken by Allison = D / 68 (since she drove at 68 mph)

Now, let's find the time it took for her brother to reach home. We know that Allison's brother drove at 54 mph and still had 84 miles left when Allison arrived. So, the total distance traveled by her brother can be calculated as:

Distance traveled by Brother = D - 84

And the time taken by her brother is:

Time taken by Brother = (D - 84) / 54

Since both Allison and her brother left at the same time, their travel times should be the same:

Time taken by Allison = Time taken by Brother

Therefore, we can equate the two expressions and solve for D:

D / 68 = (D - 84) / 54

Solving this equation will give us the value of D, which represents the distance Allison drove.

time = distance/speed

since the times were the same,

d/68 = (d-84)/54
d = 408