A is twice as fast in work as B is. If B can do a piece of work in 10 days, then A can do the same work in:

1. Break Down the Problem

To solve the problem, we need to establish the relationship between A and B's work rates based on the information given. We're told that A is twice as fast as B.

2. Relevant Concepts

• If B can complete a piece of work in 10 days, we can determine B’s work rate.
• A's work rate is double that of B's work rate.

3. Analysis and Detail

1. Calculate B's Work Rate:
   $\text{B's work rate} = \frac{1 \text{ work}}{10 \text{ days}} = 0.1 \text{ work per day}$

2. Calculate A's Work Rate:
   Since A is twice as fast as B, we have:
   $\text{A's work rate} = 2 \times 0.1 = 0.2 \text{ work per day}$

3. Calculate the Time A Takes to Complete the Work:
   The time taken by A to complete 1 work can be found using the formula:
   $\text{Time} = \frac{1 \text{ work}}{\text{A's work rate}} = \frac{1}{0.2} = 5 \text{ days}$

4. Verify and Summarize

By verifying the calculations, we see that if A completes twice the amount of work per day compared to B, then indeed, A can complete the same work in half the time that B takes.

Final Answer

A can do the same work in 5 days.