Mason can devour 4 slices of a pizza once every 2 minutes after eating his first slice. Find a linear function P that represents the total number of pizza slices Mason devours after t minutes assuming he can continue eating indefinitely.
Then, using your found P, find how long it will take Mason to devour 217 pizza slices.

We are given that Mason devours 4 slices of pizza every 2 minutes, starting after eating his first slice. We need to find a linear function \( P(t) \) that represents the total number of pizza slices Mason eats after \( t \) minutes.

### Step 1: Understand the situation
- Mason eats his first slice, and then he continues to eat 4 slices every 2 minutes.
- This creates a constant rate of pizza consumption after the first slice.

### Step 2: Define the rate
Mason's rate of eating is 4 slices every 2 minutes, which simplifies to a rate of 2 slices per minute. So, after the first slice, his consumption increases by 2 slices per minute.

### Step 3: Create the linear function
- Mason eats 1 slice at \( t = 0 \) (the first slice).
- Then for each minute after that, he eats 2 slices.

Thus, the total number of pizza slices Mason eats as a function of time \( t \) in minutes is:

\[
P(t) = 1 + 2t
\]

Where:
- \( P(t) \) is the total number of pizza slices after \( t \) minutes,
- \( t \) is the time in minutes.

### Step 4: Find how long it will take Mason to devour 217 pizza slices
We are given \( P(t) = 217 \). Substituting into the equation \( P(t) = 1 + 2t \):

\[
217 = 1 + 2t
\]

Now, solve for \( t \):
\[
217 - 1 = 2t
\]
\[
216 = 2t
\]
\[
t = \frac{216}{2} = 108
\]

### Final Answer:
It will take Mason **108 minutes** to devour 217 pizza slices.

Would you like a more detailed explanation or have any further questions?

---

Here are 5 related questions you might find interesting:
1. How many slices will Mason eat in the first 10 minutes?
2. If Mason takes a 5-minute break every 30 minutes, how many slices will he eat in 2 hours?
3. What is the slope of the linear function \( P(t) \), and what does it represent in this scenario?
4. How would the function change if Mason started eating with 2 slices instead of 1 at \( t = 0 \)?
5. If Mason could only eat for 50 minutes, how many slices would he consume in that time?

**Tip:** In any problem involving constant rates, the slope of a linear function represents the rate of change—how quickly something is increasing or decreasing over time.

Mason can devour 4 slices of a pizza once every 2 minutes after eating his first slice. Find a linear function P that represents the total number of pizza slices Mason devours after t minutes assuming he can continue eating indefinitely. Then, using your found P, find how long it will take Mason to devour 217 pizza slices.

Learn how to find a linear function to represent Mason's pizza consumption rate and solve for how long it takes to devour 217 pizza slices. This problem involves algebraic concepts like linear functions and rates of change, ideal for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation