Question

A and B can complete a task in 12 days and 18 days, respectively. They begin the work together, but B leaves after 4 days. How many more days will A take to finish the remaining work?

• A. 5 1/3 days
• B. 2 3/4 days
• C. 1 1/5 days
• D. 4 3/5 days

Answer 1

Answer:

A. 5 1/3 days

A's work rate = $(\frac{1}{12})$ of the work per day.

B's work rate = $(\frac{1}{18})$of the work per day.

Together, their work rate is:

$\frac{1}{12}+\frac{1}{18}$
$=\frac{3+2}{36}$
$=\frac{5}{36}$

In the first 4 days, they complete:

$4 \times \frac{5}{36}=\frac{20}{36}=\frac{5}{9}$

Remaining work:

$1-\frac{5}{9}=\frac{4}{9}$

Now A works alone at a rate of (\frac{1}{12}) per day.

Time taken by A to finish the remaining work:

$\frac{\frac{4}{9}}{\frac{1}{12}}$
$=\frac{4}{9}\times 12$
$=\frac{48}{9}$
$=\frac{16}{3}$
$=5\tfrac{1}{3}\text{ days}$