"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?"

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 :)