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
