1. ## time......

Two taps 'a' and 'b' can fill a water tank in 9min and 12 min respectively.In what time it will be full, if 'b' starts working 2 min after 'a' starts working?...........

2. Originally Posted by wonder
Two taps 'a' and 'b' can fill a water tank in 9min and 12 min respectively.In what time it will be full, if 'b' starts working 2 min after 'a' starts working?...........
Let T denote the volume of the tank.

Then a delivers $\dfrac T9$ per minute and

b delivers $\dfrac T{12}$ per minute.

After x minutes the tank is filled:

$\dfrac T9 \cdot x + \dfrac T{12} \cdot (x-2)=T$ . Divide by T, expand the brackets, collect like terms:

$\dfrac x9 + \dfrac x{12} - \dfrac16=1~\implies~\dfrac7{36} x=\dfrac76~\implies~\boxed{x=6}$