Final answer:
To find the number of miles per hour Rosario averages on his way home, you can use the equation 2.75 = 120 / (55 + x). By substituting the given values and solving for x, we find that Rosario does not average -11.36 miles per hour on his way home.
Step-by-step explanation:
To find the number of miles per hour Rosario averages on his way home, we can use the formula:
Average Speed = Total Distance / Total Time
Given that Rosario drives 60 miles to the ice-skating rink at an average speed of 55 miles per hour, we can calculate the total time it takes for the round trip: Total Time = Total Distance / Average Speed
Since the round trip takes 2.75 hours, we can substitute the values into the equation and solve for x:
2.75 hours = (60 miles + 60 miles) / (55 miles per hour + x miles per hour)
Simplifying the equation, we have:
2.75 = 120 / (55 + x)
Now, we can cross multiply and solve for x:
2.75(55 + x) = 120
151.25 + 2.75x = 120
2.75x = 120 - 151.25
2.75x = -31.25
x = -31.25 / 2.75
x = -11.36
Since the average speed cannot be negative, we can conclude that Rosario does not average -11.36 miles per hour on his way home. Therefore, the given equation cannot be used to find x.
The correct equation to find x should be:
2.75 = 120 / (55 + x)