An electric appliance supplies 6000   J   min - 1 , heat to the system. If the system delivers a…

Recall the formula of the first law of thermodynamics in terms of change in internal energy and work done by the system, $\Delta U=Q-W$, given, $\Delta U=2500 \mathrm{J}$, $Q=\frac{6000}{60}\times t=\left(100t \right) \mathrm{J}$ and $W=P\times t=90t$, 
$$\begin{gathered} \Rightarrow 2500 \mathrm{J}=100t \mathrm{J}-90t \mathrm{J} \\ \Rightarrow t=2.5\times {10}^2 \mathrm{s} \end{gathered}$$.