Answer
$F_s=29.1\ gal/year$
Work Step by Step
$\dot{m}=1\ kg/L\times(13.3-10.5)L/min\times6min/person.day\times 4\ persond\times 365\ days$
$\dot{m}=24528\ kg/year$
$E=\dot{m}c\Delta T,\ c=4.18\ kJ/kg.°C,\ \Delta T=(42-15)°C$
$E_s=2.768\ GJ/year$
$E_s=F_s \times \epsilon\times q,\ \epsilon=0.65,\ q=146300\ kJ/gal$
$F_s=29.1\ gal/year$
$M_s=F_s\times p_f,\ p_f=\$2.80/gal$
$M_s=\$ 81.5/year$