Linear Equations Word Problems Worksheet featuring six practical math problems for students to solve.

Let's solve each problem step by step.

---

Problem 1:

David takes 3 hours to paint a room. Sara takes 6 hours to complete the same job. If they work together, how long will they take to complete the task?

#### Solution:
1. Determine the work rates:
- David's rate: He completes \( \frac{1}{3} \) of the room per hour.
- Sara's rate: She completes \( \frac{1}{6} \) of the room per hour.

2. Combined work rate:
- When working together, their combined rate is:
\[
\text{Combined rate} = \frac{1}{3} + \frac{1}{6}
\]
- Find a common denominator (6):
\[
\frac{1}{3} = \frac{2}{6}, \quad \frac{1}{6} = \frac{1}{6}
\]
\[
\text{Combined rate} = \frac{2}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2}
\]

3. Time to complete the task:
- Since their combined rate is \( \frac{1}{2} \) of the room per hour, they complete the entire room in:
\[
\text{Time} = \frac{1}{\text{Combined rate}} = \frac{1}{\frac{1}{2}} = 2 \text{ hours}
\]

Answer:
\[
\boxed{2}
\]

---

Problem 2:

Find three consecutive odd integers such that the sum of twice the first, the second, and three times the third is 152.

#### Solution:
1. Define the integers:
- Let the three consecutive odd integers be \( x \), \( x+2 \), and \( x+4 \).

2. Set up the equation:
- According to the problem:
\[
2x + (x+2) + 3(x+4) = 152
\]

3. Simplify the equation:
- Distribute and combine like terms:
\[
2x + x + 2 + 3x + 12 = 152
\]
\[
6x + 14 = 152
\]

4. Solve for \( x \):
- Subtract 14 from both sides:
\[
6x = 138
\]
- Divide by 6:
\[
x = 23
\]

5. Find the three integers:
- The integers are \( x = 23 \), \( x+2 = 25 \), and \( x+4 = 27 \).

Answer:
\[
\boxed{23, 25, 27}
\]

---

Problem 3:

Nancy bought a soft drink for $4 and 8 candy bars. She spent a total of $28. How much did each candy bar cost?

#### Solution:
1. Define the variables:
- Let the cost of each candy bar be \( c \).

2. Set up the equation:
- The total cost is the sum of the cost of the soft drink and the cost of the candy bars:
\[
4 + 8c = 28
\]

3. Solve for \( c \):
- Subtract 4 from both sides:
\[
8c = 24
\]
- Divide by 8:
\[
c = 3
\]

Answer:
\[
\boxed{3}
\]

---

Problem 4:

A rectangle is 2 m tall and 4 m wide. If its width is enlarged to 5 m without changing its perimeter, then find the new length of the rectangle.

#### Solution:
1. Calculate the original perimeter:
- The formula for the perimeter of a rectangle is:
\[
P = 2(\text{length} + \text{width})
\]
- For the original rectangle:
\[
P = 2(2 + 4) = 2 \times 6 = 12 \text{ m}
\]

2. Set up the equation for the new dimensions:
- Let the new length be \( L \).
- The new width is 5 m.
- The perimeter remains the same:
\[
2(L + 5) = 12
\]

3. Solve for \( L \):
- Divide both sides by 2:
\[
L + 5 = 6
\]
- Subtract 5 from both sides:
\[
L = 1
\]

Answer:
\[
\boxed{1}
\]

---

Problem 5:

Mary bought one seedless watermelon for $1. How many seedless watermelons can she buy for $11?

#### Solution:
1. Determine the cost per watermelon:
- Each watermelon costs $1.

2. Calculate the number of watermelons:
- With $11, the number of watermelons she can buy is:
\[
\frac{11}{1} = 11
\]

Answer:
\[
\boxed{11}
\]

---

Problem 6:

The sum of three consecutive even numbers is 156. What is the smallest number?

#### Solution:
1. Define the integers:
- Let the three consecutive even integers be \( x \), \( x+2 \), and \( x+4 \).

2. Set up the equation:
- According to the problem:
\[
x + (x+2) + (x+4) = 156
\]

3. Simplify the equation:
- Combine like terms:
\[
3x + 6 = 156
\]

4. Solve for \( x \):
- Subtract 6 from both sides:
\[
3x = 150
\]
- Divide by 3:
\[
x = 50
\]

Answer:
\[
\boxed{50}
\]

---

Final Answers:

1. \(\boxed{2}\)
2. \(\boxed{23, 25, 27}\)
3. \(\boxed{3}\)
4. \(\boxed{1}\)
5. \(\boxed{11}\)
6. \(\boxed{50}\)