https://file.aiquickdraw.com/mathbot/file/1732363904533vpx0hnjq.jpg

Let’s solve each question step by step.

---

### **Question 1**
Walter currently runs the 40-yard dash in $ 7.2 $ seconds. He believes he can reduce his time by $ 0.2 $ seconds per week. We are tasked to find an expression for his time after $ w $ weeks.

#### Step 1: Write the equation
Each week, Walter’s time decreases by $ 0.2w $. After $ w $ weeks, his time will be:
\[
\text{Time} = 7.2 - 0.2w
\]

**Answer: D. $ 7.2 - 0.2w $**

---

### **Question 2**
A piece of yarn 4 yards long is cut in half, and each half is cut into fourths. We need to determine the length of each piece in **inches**.

#### Step 1: Convert 4 yards to inches
Since $ 1 \, \text{yard} = 36 \, \text{inches} $, $ 4 \, \text{yards} $ equals:
\[
4 \times 36 = 144 \, \text{inches}.
\]

#### Step 2: Cut into halves
Cutting 144 inches in half gives:
\[
\frac{144}{2} = 72 \, \text{inches}.
\]

#### Step 3: Cut each half into fourths
Each half of 72 inches is divided into 4 parts:
\[
\frac{72}{4} = 18 \, \text{inches}.
\]

**Answer: B. $ 18 \, \text{inches} $**

---

### **Question 3**
A ride-sharing service charges a base fee of $ \$2.40 $ per ride and $ \$0.30 $ per mile. Edward paid $ \$3.60 $ for one ride. We need to calculate the number of miles Edward rode.

#### Step 1: Write the cost equation
The total cost is:
\[
\text{Cost} = \text{Base fee} + (\text{Cost per mile} \times \text{Miles})
\]
Substitute the known values:
\[
3.60 = 2.40 + 0.30 \times \text{Miles}.
\]

#### Step 2: Solve for miles
Subtract $ 2.40 $ from both sides:
\[
3.60 - 2.40 = 0.30 \times \text{Miles}.
\]
\[
1.20 = 0.30 \times \text{Miles}.
\]
Divide by $ 0.30 $:
\[
\text{Miles} = \frac{1.20}{0.30} = 4.
\]

**Answer: C. $ 4 \, \text{miles} $**

---

### **Question 4**
Tiki cycled 13 fewer miles than Irina, and together they cycled 51 miles. We need to find how many miles Irina cycled.

#### Step 1: Let Irina’s miles be $ x $
Tiki cycled $ x - 13 $ miles. Together, they cycled 51 miles:
\[
x + (x - 13) = 51.
\]

#### Step 2: Solve for $ x $
Simplify:
\[
2x - 13 = 51.
\]
Add 13 to both sides:
\[
2x = 64.
\]
Divide by 2:
\[
x = 32.
\]

Irina cycled 32 miles.

**Answer: B. $ 32 \, \text{miles} $**

---

Would you like further clarification or detailed explanations for any step? Here are related concepts:

1. How can we generalize the reduction in time in Question 1 for non-linear improvements?
2. How do unit conversions (yards to inches) apply in larger contexts?
3. How could Question 3 change if Edward had a discount on the base fee?
4. How can systems of equations be used to solve similar problems like Question 4?

**Tip:** Always double-check unit conversions in measurement problems—they’re a common source of errors!

Solve the following math problems from the uploaded image: 1. Walter's training schedule, 2. Yarn length, 3. Ride-sharing cost, and 4. Cycling distance.

Explore solutions to linear equations, unit conversions, and distance problems. Learn how Walter reduces his 40-yard dash time, calculate yarn length in inches, analyze ride-sharing costs, and determine cycling distances. Ideal for students in Grades 6-8.

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