Assuming the tubs are equally full of water (each mass M) then it is just delta T of cold tub x M = delta T of the warm tubs x 2M. Where delta T is T -10 for the cold an 50-T for the hot ones. It does not matter what material connects the tubs in the long term, but the pipe with the highest conductivity will just cool that tub a little faster but eventually it will all even out.

The formulas you had with k A over L x delta T are for heat transfer rates but because the tubs are changing T you need a diff eqn to get the T as a function of time AND the flows are NOT equal, I don't think you use these equations for this type of question.

Assuming the tubs are equally full of water (each mass M) then it is just delta T of cold tub x M = delta T of the warm tubs x 2M. Where delta T is T -10 for the cold an 50-T for the hot ones. It does not matter what material connects the tubs in the long term, but the pipe with the highest conductivity will just cool that tub a little faster but eventually it will all even out.

The formulas you had with k A over L x delta T are for heat transfer rates but because the tubs are changing T you need a diff eqn to get the T as a function of time AND the flows are NOT equal, I don't think you use these equations for this type of question.

If you were keeping tub 1 at 50C forever and tub 2 at 10C forever, then you could calculate the heat transfer rate with your formulas!