Two pipes A and B can fill an empty tank independently in 3 hours and 4 hours, respectively. If the pipes A and B are opened in alternate hours starting with B, then the total time taken, in hours, to fill the tank is

A and B can fill the tank in 3 hours and 4 hours respectively.
Let the capacity of the tank be 12 units (LCM of 3 and 4)
Efficiency of A = $$\dfrac{12}{3} = 4$$ units/hour.

Efficiency of B = $$\dfrac{12}{4} = 3$$ units/hour.

If A and B are open every alternate hour starting with B, then in 2 hours, 7 units of the tank is filled.
Remaining capacity = 12-7 = 5 units.
3 units will be filled by B in 1 hour.
Remaining 2 units will be filled by A in $$\dfrac{1}{2}$$ hour.

Therefore, Total tank is filled in $$2+1+\dfrac{1}{2} = 3\dfrac{1}{2}$$ hours.