- Identify the total time (\(60\) minutes) and time spent on Part 1 (\(20\) minutes) to set up the equation: \(20 + m = 60\).
- Solve for \(m\) by subtracting \(20\) from both sides: \(m = 60 - 20\).
- Determine that the time remaining is \(40\) minutes.
- The correct option is \(\boxed{20 + m = 60; m = 40 \text{ minutes}}\).
Explanation
- Analyzing the Problem Data
The objective is to find the equation representing the time left for the second part of a math exam and solve for that time. Ryan has a total of 60 minutes for the entire exam. He spends 20 minutes on Part 1 and the remaining time, represented by \(m\), on Part 2. The total time for the exam is the sum of the time spent on each part.
- Formulating the Equation
The relationship between the time spent on the parts of the exam and the total time is defined as:
\[\text{Time for Part 1} + \text{Time for Part 2} = \text{Total Time}\]
Substituting the known values, we have:
\[20 + m = 60\]
This equation models the scenario where \(20\) is the time spent on Part 1, \(m\) is the time spent on Part 2, and \(60\) is the total time allotted for the exam.
- Solving for the Unknown Variable
To solve for \(m\), we isolate the variable \(m\) on one side of the equation. We subtract \(20\) from both sides of the equation:
\[20 + m - 20 = 60 - 20\]
\[m = 40\]
Therefore, Ryan had 40 minutes left for the second part of the exam. The correct equation and result are represented by the option \(20 + m = 60; m = 40\) minutes.
Examples
This type of problem is fundamental in planning and time management. For example, if you are planning to spend a total of 2 hours (120 minutes) cooking a three-course meal, and you already know that the dessert preparation will take 30 minutes, you can use a similar equation to determine how much time you have remaining for the appetizers and main course: \(30 + m = 120\). Solving this gives \(m = 90\) minutes, helping you effectively allocate your remaining time. Learning to formulate these equations allows you to manage resources and time efficiently in everyday life.