Question

a worker A finishes a project on his own in 12 days. the worker completes the same work alone in 16 days. the two workers started working together, but after 3 days A leaves and B. continues on his own. How many days will B need to finish the rest of the work?

Answer 1

Answer:

Worker B needs 9 days to finish the rest of the work

Step-by-step explanation:

Proportions

Worker A finishes a project on his own in 12 days and worker B does the same in 16 days.

Worker A does 1/12 of the project in one day and worker B does 1/16 of the project in one day. When working together, they do

$\frac{1}{12}+\frac{1}{16}=\frac{7}{48}$

After 3 days they have completed:

$3*\frac{7}{48}=\frac{7}{16}$

parts of the project, this means it still remains:

$1-\frac{7}{16}=\frac{9}{16}$

parts of the project and it is done by B alone. Since B does $\frac{1}{16}$ per day, he now takes

$\displaystyle \frac{\frac{9}{16}}{\frac{1}{16}}=9$

days to complete the project.

Worker B needs 9 days to finish the rest of the work