Each week, Rosario drives to an ice-skating rink that is 60 miles away. The round-trip takes 2.75 hours. If he averages 55 miles per hour on his way to the rink, which equation can be used to find [tex]$x$[/tex], the number of miles per hour he averages on his way home?
[tex]$\frac{60}{55}+\frac{60}{x}=2.75$[/tex]
[tex]$(\frac{60}{55})(\frac{60}{x})=2.75$[/tex]
[tex]$60(55)+60 x=2.75$[/tex]
[tex]$[60(55)](60 x)=2.75$[/tex]
Answer (2)
Calculate the time to the rink: 55 60 .
Calculate the time back home: x 60 .
Set up the equation: 55 60 + x 60 = 2.75 .
The correct equation is: 55 60 + x 60 = 2.75 .
Explanation
Problem Analysis Let's analyze the problem. We are given the distance to the ice-skating rink (60 miles), the total time for the round trip (2.75 hours), and the average speed on the way to the rink (55 miles per hour). We need to find an equation that can be used to find the average speed on the way home, which we'll call x .
Setting up the Equation The time it takes to travel to the rink is the distance divided by the speed, which is 55 60 hours. The time it takes to travel back home is the distance divided by the speed, which is x 60 hours. The total time for the round trip is the sum of these two times, so we have the equation 55 60 + x 60 = 2.75 .
Finding the Correct Equation Therefore, the correct equation is 55 60 + x 60 = 2.75 .
Examples
Understanding how to calculate travel times and average speeds is useful in many real-life situations. For example, if you're planning a road trip, you can use this type of calculation to estimate how long it will take to reach your destination, taking into account different speeds on different parts of the journey. This helps in planning your stops and managing your time effectively. Imagine you are driving to a city 150 miles away. You drive the first 75 miles at 60 mph and want to know how fast you need to drive the remaining distance to arrive in exactly 2.5 hours. You can set up an equation similar to the one in this problem to solve for the required speed.
The correct equation to find Rosario's average speed on his way home is 55 60 + x 60 = 2.75 . This equation combines the time taken for both trips. It allows us to solve for x , the return speed.
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