A can finish a job in 8 hours and B can finish the same job in 12 hours independently. If they work simultaneously, in how many hours can they do the same job?

The correct option is 4.8.

To find the total time taken by A and B to complete the job when working simultaneously, we can calculate their individual work rates first:

The work rate of A, who finishes the job in 8 hours, is:
$R_A=\frac{1}{8}$ of the job per hour.

The work rate of B, who finishes the job in 12 hours, is:
$R_B=\frac{1}{12}$ of the job per hour.

When working simultaneously, their combined work rate ($R_{\text{combined}}$) is the sum of their individual rates:
$R_{\text{combined}}=\frac{1}{8}+\frac{1}{12}$

To add these fractions, find the least common multiple (LCM) of 8 and 12, which is 24:
$R_{\text{combined}}=\frac{3}{24}+\frac{2}{24}=\frac{5}{24}$ of the job per hour.

The time required to finish the complete job when working together is the reciprocal of their combined work rate:
$\text{Time}=\frac{24}{5}=4.8$ hours.

Thus, they can finish the same job in 4.8 hours when working together.