Answer
28 minutes
Work Step by Step
We first must find how much energy is needed to bring the water to a boil:
$Q = mc\Delta t = (2.5)(4184)(90)=941,400\ J \approx 941 \ kJ$
Recall, the energy supplied is equal to the integral of P with respect to time. Note, we must substitute a "dummy variable" in for t, for the same variable cannot be in both the expression and in the bounds of the integral. Thus, we find:
$ 941 = \int_0^t 1.1 + 2.3 s$
$ 0 = 1.15t^2 + 1.1t -941 $
Using either a calculator or the quadratic formula, we obtain:
$ t = 28 \ min$
