A can complete a piece of work in 40 days. A and B together can complete the same work in 8 days. In how many…

Question

A can complete a piece of work in 40 days. A and B together can complete the same work in 8 days. In how many days can B alone complete the work?

ScanSolve AI Tutor · Accepted Answer

here's the solution to this work-rate problem:

Determine the individual work rate of A.
A can complete the work in 40 days. So, A's one-day work rate is $\frac{1}{40}$ of the total work.
Determine the combined work rate of A and B.
A and B together can complete the work in 8 days. So, their combined one-day work rate is $\frac{1}{8}$ of the total work.
Set up the equation to find B's work rate.
The combined work rate of A and B is the sum of their individual work rates. Let B's one-day work rate be $\frac{1}{T_B}$ , where $T_B$ is the time B takes to complete the work alone.
$\frac{1}{40} + \frac{1}{T_B} = \frac{1}{8}$
Solve for B's one-day work rate.
Subtract A's work rate from the combined work rate:
$\frac{1}{T_B} = \frac{1}{8} - \frac{1}{40}$
Find a common denominator, which is 40:
$\frac{1}{T_B} = \frac{5}{40} - \frac{1}{40}$ $\frac{1}{T_B} = \frac{5 - 1}{40}$ $\frac{1}{T_B} = \frac{4}{40}$ $\frac{1}{T_B} = \frac{1}{10}$
Determine the time B takes to complete the work alone.
Since B's one-day work rate is $\frac{1}{10}$ , B will take 10 days to complete the work alone.
$T_B = 10 \text{ days}$
The final answer is $\text{} 10 \text{ days} \text{}$

A can complete a piece of work in 40 days. A and B together can complete the same work in 8 days. In how many days can B alone complete the work?