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This problem is a classic work-rate problem. Let's break it down step by step:

### Problem Statement:
- **Mario** had been working alone for 1 hour when **Karlo** joined him.
- Together, they were able to finish the **remaining portion** of the job in 3 hours.
- **Mario** can finish the job **2 hours longer** than **Karlo** can finish the job on his own.

### Goal:
We need to find how long it would take **Mario** to finish the job if he worked alone.

---

### Step 1: Define Variables
Let:
- \( M \) = Time taken by Mario to finish the entire job alone (in hours).
- \( K \) = Time taken by Karlo to finish the entire job alone (in hours).

We are told:
1. Mario takes 2 hours longer than Karlo: 
   \[
   M = K + 2
   \]
   
2. Work-rate is the portion of work done per unit time, so:
   - Mario's work rate is \( \frac{1}{M} \) jobs per hour.
   - Karlo's work rate is \( \frac{1}{K} \) jobs per hour.

### Step 2: Analyze the Work Done
- Mario works alone for 1 hour. In that 1 hour, Mario completes:
  \[
  \text{Work done by Mario in 1 hour} = \frac{1}{M}
  \]
  So, after 1 hour, the remaining portion of the job is:
  \[
  1 - \frac{1}{M} = \frac{M-1}{M}
  \]

- Then, Mario and Karlo together finish the remaining job in 3 hours. Their combined work rate is:
  \[
  \frac{1}{M} + \frac{1}{K}
  \]
  So, in 3 hours, they complete:
  \[
  3 \left( \frac{1}{M} + \frac{1}{K} \right) = \frac{M-1}{M}
  \]

### Step 3: Set Up the Equation
Using the equation from the second part of the work:
\[
3 \left( \frac{1}{M} + \frac{1}{K} \right) = \frac{M-1}{M}
\]

Substitute \( K = M - 2 \) into the equation:
\[
3 \left( \frac{1}{M} + \frac{1}{M-2} \right) = \frac{M-1}{M}
\]

### Step 4: Solve the Equation
Let’s solve the equation to find \( M \). I'll compute that now.The solutions to the equation are \( M = 1 \) and \( M = 8 \).

However, \( M = 1 \) doesn't make sense in the context of the problem because it implies Mario would finish the entire job in 1 hour, which contradicts the problem's conditions. Therefore, the correct solution is:

\[
M = 8 \text{ hours}
\]

So, it would take Mario 8 hours to finish the job alone.

---

Would you like more details or have any questions?

Here are 5 related questions you could explore:
1. How long would it take for Karlo to complete the job alone?
2. How much work did Mario finish before Karlo joined him?
3. What is the combined work rate of Mario and Karlo when working together?
4. What portion of the job did Mario complete in the first hour?
5. If Karlo joined after 2 hours instead of 1, how would the total time change?

**Tip:** In work-rate problems, always express the rates in terms of "jobs per hour" to set up the correct equations easily.

Mario had been working for 1 hour when Karlo joined him and they were able to finish the remaining portion of the job in 3 hours. If Mario can finish the job 2 hours longer than Karlo, how long would it take him to finish the job alone?

Learn how to solve a work-rate problem involving Mario and Karlo. This problem explores how long it would take Mario to finish a job alone after working together with Karlo. We use key algebraic concepts and work-rate formulas. Suitable for students in Grades 9-12.

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