A can complete a work in 12 days, and B can complete the same work in 16 days. If A and B work together for 4 days and then B leaves, how many more days will A need to finish the r

Problem

A can complete a work in 12 days, and B can complete the same work in 16 days. A and B work together for 4 days, then B leaves. Find how many more days A will need to finish the remaining work.

Solution

Step 1: Work done by A and B per day

A's 1 day work: $\frac{1}{12}$
B's 1 day work: $\frac{1}{16}$

Work done together in 1 day: $\frac{1}{12}+\frac{1}{16}=\frac{7}{48}$

Step 2: Work done by A and B in 4 days

$4\times \frac{7}{48}=\frac{28}{48}=\frac{7}{12}$

Remaining work: $1-\frac{7}{12}=\frac{5}{12}$

Step 3: Days required by A to finish remaining work

$\text{Days}=\frac{\frac{5}{12}}{\frac{1}{12}}=5$

Answer

$\boxed{5\text{ days}}$