Welcome to Johnmiedema.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Explore in-depth answers to your questions from a knowledgeable community of experts across different fields. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

## Sagot :

**Answer:**

5 hours and 48 minutes

**Step-by-step explanation:**

The **equation** for finding **average speed **is: [tex]\frac{\text{Total Distance}}{\text{Total Time}}[/tex]

Let **x **represent the distance for **both** the journey from Riley's college to home and back. We can use **one variable** to represent this because both distances are the **same**.

We also know that the total round trip took **12 hours**. Let **y** represent the time it took for Riley to drive from college to home. Therefore the time it takes for Riley to drive from home to college is **12 - y**.

Using this information, we can set up a **system of equations**.

### Setting up a System of Equations

[tex]65.1=\frac{x}{y}\\\\69.6=\frac{x}{12-y}[/tex]

Multiply **both sides** of the first equation by "y" and both sides of the second equation by "12 - y".

[tex]65.1y=x\\\\835.2-69.6y=x[/tex]

Since both 65.1y and 835.2-69.6y are equivalent to x, we can set them equal to **each other**.

[tex]65.1y=835.2-69.6y[/tex]

Now, we have to **solve the equation **for time or "y".

### Solving for Time

[tex]65.1y=835.2-69.6y[/tex]

Add 69.6y to** both sides**

[tex]65.1y+69.6y=835.2[/tex]

[tex]134.7y=835.2[/tex]

Divide both sides by 134.7

[tex]y\approx6.2 $ hours = Six hours Twelve Minutes[/tex]

This is the time it took for Riley to drive from college to home, therefore the time it took for Riley to drive from home back to college is:

[tex]12-6.2=5.8=5$ hours and 48 minutes[/tex]

**5 hours and 48 minutes**