Question

"You want to cook 250g of pasta (the pasta is at 20 degrees C originally). The instructions say to boil 2L of water, then place the dry pasta into the water. a) If the specific heat of the pasta is 1800J.kg-1.K-1, and the specific heat of water is 4186j.kg-1.k-1, what is the temperature of the water immediately after the pasta is added to the vigorously boiling water?"
So, I didn't know how to include time into this so I made the assumption that the whole system was in equilibrium immediately after the pasta was added. I took the equation
Q=cmDeltaT and set it to equal to 0, and came with this equation
c(pasta)*m(pasta)*Ti(pasta)-c(pasta)*m(pasta)*Tf(pasta) = - c(water)*m(water)*Ti(water)-c(water)*m(water)*(Tf(water).

After plugging in my numbers (at some point, I equated Tf(pasta) to Tf(water) because I was assuming they were in equilibrium) and got -98.4 degrees Celsius. Is there any other way to do this?

For b), The question asks how long the water will take to return to a boil if the burner is supplying 1 kW to the pot. I'm not even sure where to start with this one. Even an equation with a time component would be appreciated.

Thank you in advance :)