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### Problem Recap:
- You start with 785 bricks to move.
- You move a few bricks by hand, then decide to use a wheelbarrow, moving 5 wheelbarrows per hour.
- After 4 hours of using the wheelbarrow, you have moved 245 bricks.
- After 6 hours, you have moved 365 bricks.

#### Step 1: Calculate the number of bricks moved per hour using the wheelbarrow.
You are given two points:
- After 4 hours, you've moved 245 bricks.
- After 6 hours, you've moved 365 bricks.

This indicates that in 6 - 4 = 2 hours, you moved 365 - 245 = 120 bricks.

So, the number of bricks moved per hour (slope) is:

\[
\frac{120 \, \text{bricks}}{2 \, \text{hours}} = 60 \, \text{bricks/hour}.
\]

You are moving **60 bricks per hour** using the wheelbarrow.

#### Step 2: Determine how many bricks you moved by hand before using the wheelbarrow.
At 4 hours, you have moved 245 bricks using the wheelbarrow. You are using the wheelbarrow from the start of the 4th hour. Therefore, the bricks moved before using the wheelbarrow (moved by hand) would be **245 bricks**.

#### Step 3: Write a linear function.
The linear function has the form:

\[
Q(t) = mt + b,
\]
where:
- \( Q(t) \) is the number of bricks moved after \( t \) hours,
- \( m = 60 \) (the slope, or number of bricks moved per hour using the wheelbarrow),
- \( b = 245 \) (the initial number of bricks moved by hand).

Thus, the linear function is:

\[
Q(t) = 60t + 245.
\]

#### Step 4: Find the value of \( t \) when \( Q(t) = 785 \).
We are asked to find the time \( t \) when all 785 bricks are moved.

Set \( Q(t) = 785 \):

\[
785 = 60t + 245.
\]

Now, solve for \( t \):

\[
785 - 245 = 60t \implies 540 = 60t \implies t = \frac{540}{60} = 9 \, \text{hours}.
\]

So, it will take 9 hours to move all the bricks.

#### Step 5: Explain the meaning of the ordered pair.
The ordered pair \( (9, 785) \) means that after 9 hours, you will have moved all 785 bricks to the backyard.

---

### Summary:
1. You are moving **60 bricks per hour** using the wheelbarrow.
2. You moved **245 bricks** by hand before using the wheelbarrow.
3. The linear function is \( Q(t) = 60t + 245 \).
4. You will move all the bricks in **9 hours**.
5. The ordered pair \( (9, 785) \) means that after 9 hours, all 785 bricks will have been moved.

Would you like more details or have any other questions?

### Five related questions:
1. How would the equation change if you moved fewer bricks by hand initially?
2. What if the total number of bricks was more than 785?
3. How would the time change if you moved 70 bricks per hour with the wheelbarrow?
4. Can you express this situation as a piecewise function to account for the hand-moving part?
5. How would the graph of the function \( Q(t) = 60t + 245 \) look?

### Tip:
When solving word problems involving linear functions, always identify the slope (rate of change) and intercept (initial value) carefully.

You have 785 decorative bricks delivered to your house and set down in your driveway. You need to move all of the bricks to your backyard. You move a few bricks by hand and quickly decide that will take forever, so you go buy a wheelbarrow to haul the rest. You decide to pace yourself by hauling 5 wheelbarrows full of bricks each hour. After 4 hours, you determine that you have moved 245 bricks to the back yard. After 6 hours, you find you have moved 365 bricks to the back yard.

Solve a linear function word problem involving moving bricks with a wheelbarrow. Learn how to calculate the rate of bricks moved per hour, write a linear equation in the form Q(t) = mt + b, and determine how long it takes to move all 785 bricks. Suitable for students in Grades 8-10.

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