Allison drove home at 60 mph, but her brother Austin, who left at the same time, could drive at only 48 mph. When Allison arrived, Austin still had 60 miles to go. how far did Allison drive?

Let's solve the problem step by step.

### Step 1: Define Variables
- Let the distance that Allison drove be \( d \) miles.
- Let the time it took Allison to drive home be \( t \) hours.

### Step 2: Express the Distance and Time Relationships
- Since Allison drove at 60 mph, the relationship between the distance \( d \) and time \( t \) can be expressed as:
  \[
  d = 60t
  \]

- Austin drove at 48 mph for the same amount of time \( t \), so the distance Austin drove can be expressed as:
  \[
  \text{Distance Austin drove} = 48t
  \]

### Step 3: Set Up the Equation
- According to the problem, when Allison arrived home, Austin still had 60 miles to go. This means the total distance Austin needed to drive is \( 48t + 60 \) miles.

- But since Austin left at the same time as Allison and has 60 miles left when Allison arrived, the distance Allison drove \( d \) must equal the total distance Austin needed to drive:
  \[
  d = 48t + 60
  \]

### Step 4: Substitute and Solve
- Substitute the expression for \( d \) from the first equation into the second equation:
  \[
  60t = 48t + 60
  \]

- Subtract \( 48t \) from both sides:
  \[
  12t = 60
  \]

- Solve for \( t \):
  \[
  t = \frac{60}{12} = 5 \text{ hours}
  \]

### Step 5: Calculate the Distance
- Now, use the value of \( t \) to find the distance Allison drove:
  \[
  d = 60t = 60 \times 5 = 300 \text{ miles}
  \]

### Final Answer
Allison drove **300 miles**.

Would you like more details or have any questions?

Here are some related questions to explore:
1. How long would it take Austin to finish his journey after Allison arrived?
2. If Allison had driven 10 mph faster, how much time would she save?
3. What if Austin had started his journey 30 minutes earlier, how far would he be when Allison arrives?
4. If both had driven for an additional 2 hours, how much further would Allison be from Austin?
5. What if Austin's speed was reduced by 10 mph after half of the journey, how far would he be when Allison arrives?

**Tip:** When solving problems involving speed, time, and distance, always start by identifying the relationships and equations linking these variables.

Allison drove home at 60 mph, but her brother Austin, who left at the same time, could drive at only 48 mph. When Allison arrived, Austin still had 60 miles to go. How far did Allison drive?

Discover how to solve a real-life distance problem involving Allison driving at 60 mph and Austin driving at 48 mph. This step-by-step guide covers linear equations and the relationship between distance, speed, and time, suitable for Grades 6-8.

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