A can do a piece of work in 4 hours and B can do it in 6 hours. How much time would they take working together to finish the work?

5 hours

Step-by-step explanation:

A = 4hours

B = 6 hours

Average of A and B = (4hours+6hours) / 2 = 5hours

2.4 hours

Step-by-step explanation:

Let total work = X

Rate of work done = X : time

Rate of A = X/4

Rate of B = X/6

If they work together, rate is the sum of their individual rates, i. e.

X/4 + X/6

= (3X + 2X) / 12 (taking LCM)

=5X/12

Rate = X/time

5X/12 = X/time

time = X: (5X/12)

time = X * 12 / (5X)

time = 2.4 hours

Shortcut:

Product of individual times/sum of individual times

= (4*6) / (4+6)

=24/10

=2.4 hours