#### Answer

14 minutes

#### Work Step by Step

We first find the amount of energy needed to melt the snow. Thus, we use the heat of fusion of snow to find:
$Q = (5kg)(334,000) = 1,670,000 J$
We know that the power is a rate, so we take the energy to find how much energy is needed. Doing this, we find how long it will take to reach this temperature:
$1,670,000 = \int_0^t (a+ bT)dT$
(Note, we have to use "T" instead of "t": this does not change the answer, but we must do it since we are not allowed to have the same variable in the limits and in the function being integrated.)
Thus, we find:
$1,670,000 = (1,100)t + 1.15t^2 $
$ t \approx 14 \ minutes$