Answer
It will take 402 seconds to boil the water.
Work Step by Step
We can find the mass of the water as:
$m = \rho~V$
$m = (1000~kg/m^3)(0.75~L)(\frac{10^{-3}~m^3}{1~L})$
$m = 0.75~kg$
We can find the energy required to raise the temperature of the water by $89^{\circ}C$;
$Q_w = mc~\Delta T$
$Q_w = (0.75~kg)(4186~J/kg~C^{\circ})(89^{\circ}C)$
$Q_w = 279,415.5~J$
We can find the energy required to raise the temperature of the aluminum by $89^{\circ}C$;
$Q_a = mc~\Delta T$
$Q_a = (0.280~kg)(900~J/kg~C^{\circ})(89^{\circ}C)$
$Q_a = 22,428~J$
We can find the total amount of energy required as:
$Q = Q_w+Q_a$
$Q = 279,415.5~J+22,428~J$
$Q = 301,843.5~J$
We can find the time required for the coffeepot to produce this amount of energy as:
$t = \frac{Q}{P}$
$t = \frac{301,843.5~J}{750~W}$
$t = 402~seconds$
It will take 402 seconds to boil the water.