B is twice as good a workman as A. If A completes a work in 28 days, how much work will be completed in 4 days if A and B work together on the same piece of work?
Understand the Problem
This is a work rate problem where we need to determine how much work A and B can complete together in 4 days, given that B is twice as efficient as A, and A can complete the work in 28 days. We will need to find the work rate of each individual and then combine them to find the answer.
Answer
$\frac{3}{7}$
Answer for screen readers
The work completed in 4 days if A and B work together is $\frac{3}{7}$.
Steps to Solve
- Find the work rate of A
If A completes the work in 28 days, A's work rate is $1/28$ of the work per day.
- Find the work rate of B
Since B is twice as efficient as A, B's work rate is $2 \times (1/28) = 1/14$ of the work per day.
- Find the combined work rate of A and B
When A and B work together, their combined work rate is the sum of their individual work rates: $1/28 + 1/14 = 1/28 + 2/28 = 3/28$ of the work per day.
- Calculate the amount of work completed in 4 days
Multiply the combined work rate by the number of days they work together (4 days): $(3/28) \times 4 = 12/28 = 3/7$ of the work.
The work completed in 4 days if A and B work together is $\frac{3}{7}$.
More Information
The problem involves understanding rates of work and combining them to find a joint rate.
Tips
A common mistake is to not properly account for the increased efficiency of B compared to A. Also, some might forget to multiply the combined work rate by the number of days.
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