treat the 2 masses of water as separate objects. For the 52 degree water, it must undergo a temperature change of 15 degrees to reach the safe temperature of 37. Using the formula energy = mass × shc × temperature change, the energy transferred from the 19kg of 52 degree water to the mass of 21 degree water must be 19×4180×(52-37)=1191300j
now we know that the energy change of the 21 degree water is also 1191300 because, assuming no energy is dissipated, energy must be conserved in the system. So we know the energy, the specific heat capacity and the temperature change (37-21). By rearranging the above formula, e=mct we get m=e/ct
putting in numbers we arrive at 1191300/(4180×(37-21))=17.8125
since this is isaac physics they're very picky about significant figures so check what degree of accuracy you are supplied in the question, i expect 2 or 3 significant figures giving you a result of 18kg or 17.8kg
Sorry now I've looked on isaac I know what I did wrong, basically it's exactly the same method but swap around the temperatures. I took it to be 19kg of 51°C water but it's actually 19kg of 21°C water