Answer
$m_{vapor}=1 \text{ kg/day}$ $Q_{latent}=2450\text{ kJ/day}$
Work Step by Step
The amount of moisture produced per day is $$
\begin{aligned}
\dot{m}_{\text {vapor }} & =(\text { Moisture produced per person })(\text { No. of persons }) \\
& =(0.25 \mathrm{~kg} / \text { person })(4 \text { persons } / \text { day })=1 \mathrm{~kg} / \text {day }
\end{aligned}
$$ Then the latent heat load due to showers becomes $$
\dot{Q}_{\text {latent }}=\dot{m}_{\text {vapor }} h_{\text {fg }}=(1 \mathrm{~kg} / \text { day })(2450 \mathrm{~kJ} / \mathrm{kg})=\mathbf{2 4 5 0}\ \mathbf{k J} / \text {day }
$$
