A can complete a piece of work in 4 hours and B can complete it in 6 hours. In how much time (in hours) will they together complete the work?

The correct answer is 2 hours 24 minutes.

To find the time taken by A and B to complete the work together, we can determine their individual rates of work per hour.

A can complete the work in 4 hours, which means A's work rate per hour is:
$\frac{1}{4}$
of the total work.

Similarly, B can complete the work in 6 hours, which means B's work rate per hour is:
$\frac{1}{6}$
of the total work.

When working together, their combined work rate per hour is the sum of their individual rates:
$\text{Combined rate}=\frac{1}{4}+\frac{1}{6}$

To add these fractions, we find the least common multiple (LCM) of 4 and 6, which is 12:
$\frac{1}{4}+\frac{1}{6}=\frac{3}{12}+\frac{2}{12}=\frac{3+2}{12}=\frac{5}{12}$

Thus, they together complete:
$\frac{5}{12}$
of the work in 1 hour.

The total time required for them to complete the entire work together is the reciprocal of their combined rate:

Now, let us convert this value into hours and minutes:
$\frac{12}{5}\text{hours}=2\frac{2}{5}\text{hours}=2\text{hours}+(\frac{2}{5}\times 60)\text{minutes}$

Calculating the minutes:
$\frac{2}{5}\times 60=2\times 12=24\text{minutes}$

Therefore, they will complete the work together in 2 hours 24 minutes.