Thanks but it isn't said how to do it, it's the question. Obviously there is a trick in it otherwise it cannot be done as you said correctly.
Solve for m.
In the end we are getting as much heat as possible out of the mass m. We can always presume we are doing this with less than perfect efficiency and require more than this mass, but certainly no less than it.
Where did you find the question?
Another possibility is that the hot water is gas, but the cold water is still liquid: it takes energy in order to change from state to state, so when you put heat energy into water it sort of gets stuck at 100 degrees until it actually boils.
It is a bit of a silly assumption to make though... but the only possibility that springs to mind, unless that specific heat capacity of pure water really is much greater than the specific heat capacity of mineral water. I really doubt this though: after all, mineral water has more stuff in it than pure water, so I would of thought mineral water had a higher specific heat capacity.