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The problem in the image asks to find the number of days A and B together would take to complete a task, given that A is 6 times more efficient than B, and B takes 32 days to complete the task alone.

### Step-by-step solution:

1. **Efficiency of B:**
   B can complete the task in 32 days. So, in one day, B completes \( \frac{1}{32} \) of the task.

2. **Efficiency of A:**
   A is 6 times more efficient than B, so A completes \( 6 \times \frac{1}{32} = \frac{6}{32} = \frac{3}{16} \) of the task per day.

3. **Combined efficiency of A and B:**
   Together, A and B will complete \( \frac{1}{32} + \frac{3}{16} \) of the task per day. To simplify:
   \[
   \frac{3}{16} = \frac{6}{32}
   \]
   So, combined, they complete:
   \[
   \frac{1}{32} + \frac{6}{32} = \frac{7}{32}
   \]
   of the task in one day.

4. **Time taken to complete the task:**
   The fraction of the task completed per day is \( \frac{7}{32} \). So, the number of days required to complete the task is the reciprocal of \( \frac{7}{32} \), which is:
   \[
   \frac{32}{7} \approx 4.57 \text{ days}.
   \]

Since the closest option is **5 days**, the answer should be **rounded** to 5 days.

Would you like more details or have any questions?

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Here are some related questions to expand your understanding:

1. How does increasing A's efficiency affect the total number of days required to complete the task?
2. If A was only 3 times more efficient than B, how many days would it take them to complete the task together?
3. What would happen if A and B were equally efficient?
4. How can you generalize the formula to calculate the total time for different efficiency ratios between A and B?
5. If B's efficiency decreases and now takes 40 days to finish the task alone, how would that impact the total time with A?

**Tip:** Always check units (days, hours, etc.) and ensure that your final answer has the correct units!

If A is 6 times more efficient than B and B takes 32 days to complete a task, then find the number of days required to finish the whole work by A and B working together.

Learn how to calculate the time required for A and B to complete a task together, where A is 6 times more efficient than B, and B takes 32 days to finish the task alone. Includes formulas for efficiency and work problems, suitable for students in Grades 8-10.

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