The amount of time that three people worked on a special project was in the ratio of 2 to 3 to 5. If the project took 110 hours, how many more hours did the person who worked the most hours work than the person who worked the least hours?

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the Ratios
The amount of time worked by three people is in the ratio of 2:3:5. This means:
- Person A worked for 2 parts,
- Person B worked for 3 parts,
- Person C worked for 5 parts.

### Step 2: Assign Variables
Let the number of hours each person worked be represented as:
- Person A: \(2x\)
- Person B: \(3x\)
- Person C: \(5x\)

### Step 3: Set Up the Equation
According to the problem, the total time worked by all three people is 110 hours. Therefore, we can set up the equation:
\[ 2x + 3x + 5x = 110 \]

### Step 4: Combine Like Terms
Combine the terms on the left side of the equation:
\[ 10x = 110 \]

### Step 5: Solve for \(x\)
To find \(x\), divide both sides of the equation by 10:
\[ x = \frac{110}{10} = 11 \]

### Step 6: Calculate Individual Work Hours
Now, we can find out how many hours each person worked:
- Person A: \(2x = 2 \times 11 = 22\) hours
- Person B: \(3x = 3 \times 11 = 33\) hours
- Person C: \(5x = 5 \times 11 = 55\) hours

### Step 7: Find the Difference Between Most and Least Hours
The person who worked the most hours is Person C (55 hours), and the person who worked the least hours is Person A (22 hours). To find how many more hours the person who worked the most hours worked than the person who worked the least hours, we calculate:
\[ 55 - 22 = 33 \text{ hours} \]

### Final Answer
The person who worked the most hours worked 33 hours more than the person who worked the least hours.

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