Alright, I'm a chemist but since nobody else has explained it I'll take a shot. First of all, the explanation is just confusing and junk so just ignore it for the time being. So first, you have some flow rate of water - it's passing through at 730 Mg/h. That's not a typo - it's megagrams, not milligrams. And it's at 15 degrees when it enters but has to be 120 degrees when it exits, for a change in temp of 105 degrees. That's all the information you're given.

Okay, so you want how much power is required to heat it up. Alright, so what's the units of power? It's W, or J/s. In other words, you need to find the energy needed and the time period over which that energy is supplied. Let's do the easy part first. The plant is operating at 50% capacity. So while you would expect the input stream to be flowing through at 730 Mg/h based on temperature, it's actually only half that. So 365 Mg/h. Now, since you want this in terms of J or MJ/s, you should convert hours to second right off the bat since it's an easy calculation. 365 Mg/h*(1 h/3600 s). In other words, about 0.1 Mg/s. Alright, so 0.1 Mg or 100 kg can be supplied in one second.

So the question becomes how much energy do you need to heat that 100 kg up? Well, that's just a simple specific heat capacity calculation. So you need 0.1 Mg*(1000 kg/1 Mg)*4.18 kJ/kg-degrees C*105 degrees C, which is about 40,000 kJ or 40 MJ as an estimate. Okay, so putting it together, you need 40 MJ/s, or 40 MW to do this. But wait! The heaters are only working at 40% capacity! That means that if you "think" they're supplying 100 MW, they're actually only supplying 40 MW! Thus, you want to set it to about 100 MW. So that's your answer.

You'll notice that that's not one of their answer choices and that's because they screwed up either in the question stem or in the figure. Based on the answer choices, it's probably in the figure. It should read 73 Mg/h, not 730, in the figure. That's why their explanation says 73 Mg/h and not 730 Mg/h.