C is time taken by pipe B to fill 1/3 of tank . Pipe B was kept open for half the time which is ( A/2 hrs ) required by pipe A to fill the tank by itself Wb * A/2 = filled some amount of tank pipe A was kept open for as much time as was required by the pipe B to fill up 1/3 of the tank by itself. Yeah so Wa * C hrs= Filled Some Amount of tankSo the equation is: (assuming correct work)

I would suggest - you start with a clean slate and start over.

Wa ( Per hr work by pipe A ) = 1/ A

Wb ( Per hr work by pipe B ) = 1/B

1.2(1/A + 1/B) = 1 /2

1.2 ( A + B ) = AB / 2

AB= 2.4 ( A+ B )

Wb * A/2 = kept open

Wb * C hrs = 1/ 3

Wa * C = kept open

Wb * A/2 + Wa * C = 5/6

1/3c * A/2 + C/A = 5/6

A/ 6c + C/A = 5/6

3A^2 + 2 B ^2 = 5AB

the two equations you have in A and B only

3A^2 + 2 B ^2 = 5AB

AB = 2.4 ( A+ B)

A * B = 2.4 * (A + B)

**A = 2.4 * B / (B - 2.4)**

How this step was achieved ?