) A and B together can complete a piece of work in 4 days. If A alone can complete the same work
in 12 days, in how many days can B alone complete that work?

Let's solve this problem step by step.

### Step 1: Determine the work rates of A and B together.
- A and B together can complete the work in 4 days.
- So, their combined work rate is \( \frac{1}{4} \) of the work per day.

### Step 2: Determine the work rate of A alone.
- A alone can complete the work in 12 days.
- So, A's work rate is \( \frac{1}{12} \) of the work per day.

### Step 3: Determine the work rate of B alone.
- Let B's work rate be \( \frac{1}{x} \) of the work per day, where \( x \) is the number of days B takes to complete the work alone.

Since A and B together complete \( \frac{1}{4} \) of the work per day:
\[
\text{A's rate} + \text{B's rate} = \frac{1}{4}
\]
\[
\frac{1}{12} + \frac{1}{x} = \frac{1}{4}
\]

### Step 4: Solve for \( x \).
To solve for \( x \), first subtract \( \frac{1}{12} \) from both sides of the equation:
\[
\frac{1}{x} = \frac{1}{4} - \frac{1}{12}
\]

To subtract these fractions, find a common denominator (which is 12):
\[
\frac{1}{4} = \frac{3}{12}
\]
\[
\frac{1}{x} = \frac{3}{12} - \frac{1}{12} = \frac{2}{12} = \frac{1}{6}
\]

Thus, \( x = 6 \).

### Final Answer:
B alone can complete the work in **6 days**.

Would you like more details or have any questions?

---

Here are 5 related questions for further practice:

1. If A and B together can complete a task in 5 days, and B alone can do it in 15 days, how long would it take for A alone to complete it?
2. If A, B, and C together can finish a job in 3 days, and A alone takes 6 days, while B takes 9 days, how long will C alone take to finish the job?
3. If A takes twice as long as B to finish a job, and together they finish it in 8 days, how long will it take each to finish it individually?
4. A can finish a job in 10 days, B can do the same job in 15 days, and C can do it in 20 days. How long will it take for all three to finish the job together?
5. If A alone can finish a job in 7 days, and B alone can finish it in 5 days, but A starts the job and works for 2 days before B joins, how long will it take them to complete the job together?

**Tip:** When working with rates, it's often easier to express the work done as a fraction of the whole job, as this helps in understanding combined efforts.

Learn how to solve a work rate problem involving A and B completing a task together in 4 days and A completing the task alone in 12 days. Understand the concept of work rates and solve linear equations to determine how many days B alone would take to complete the task. Suitable for students in 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