https://file.aiquickdraw.com/mathbot/file/1726597789972g558rseh.jpg

Let's go through the problem based on the image you uploaded.

### Part A: Slope of the Graph (Emma's Typing Speed)
The graph shows Emma's typing speed. The slope of the graph represents the number of words typed per minute. To calculate the slope, we need to choose two points from the graph and apply the formula:

\[
\text{slope} = \frac{\Delta y}{\Delta x} = \frac{\text{change in words}}{\text{change in time (minutes)}}
\]

From the graph, we can choose two points:
- Point 1: (1 minute, 45 words)
- Point 2: (2 minutes, 90 words)

Now calculate the slope:

\[
\text{slope} = \frac{90 - 45}{2 - 1} = \frac{45}{1} = 45
\]

So, **Emma types at a rate of 45 words per minute**.

### Part B: Time to Type a 3,600-Word Document
Now we compare the time it would take both Noah and Emma to type a 3,600-word document.

#### Noah's typing speed
Noah's typing speed is given by the equation \( y = 30x \), where \( y \) is the number of words and \( x \) is the number of minutes. So, Noah types 30 words per minute. To find how long it takes Noah to type 3,600 words:

\[
x = \frac{3600}{30} = 120 \text{ minutes}
\]

#### Emma's typing speed
From Part A, we know that Emma types 45 words per minute. To find how long it takes Emma to type 3,600 words:

\[
x = \frac{3600}{45} = 80 \text{ minutes}
\]

#### Comparing Times
- Noah takes 120 minutes.
- Emma takes 80 minutes.

Thus, **Noah takes 40 minutes longer than Emma** to type the document. Therefore, the correct statement is:

- **Noah would take 40 minutes longer to type the document than Emma.**

---

Would you like further clarification on any part? Feel free to ask!

Here are 5 related questions to deepen your understanding:
1. What would be the slope of the graph if Emma's typing speed were to increase by 10 words per minute?
2. How would the equation change if Noah improved his typing speed to 40 words per minute?
3. How many words would Emma and Noah each type in 10 minutes?
4. If Emma typed for 15 minutes, how many words would she have typed?
5. What would happen to the graph if Emma took a break in the middle of typing?

**Tip**: When interpreting graphs, always remember that the slope represents the rate of change— in this case, typing speed!

Noah's typing is represented by the equation y = 30x, where y is the number of words typed in x minutes. Emma's typing speed is represented by a graph. The graph shows the number of words typed over time. What is Emma's typing speed, and who takes longer to type a 3,600-word document?

Learn how to calculate typing speeds from both a graph and an equation. In this problem, Noah's typing speed is 30 words per minute, and Emma's is determined from the graph. We also compare the time it takes for each to type a 3,600-word document. Suitable for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation