Пусть x - скорость нагнетания воды первым насосом, пусть y - скорость нагнетания воды вторым насосом, пусть t - время. V - объём бассейна.
(x+y)*t=V; t=48/60=0,8.
xt1=y(t1+1/3)=(x+y)4/5;=> xt1=yt1+y/3=4x/5+4y/5;
\left \{ {{5xt1=4x+4y} \atop {5yt1+5y/3=4x+4y;}} \right. => \left \{ {{t1=\frac{4x+4y}{5x}} \atop {5yt1=4x+7y/3;}} \right. " alt=" \left \{ {{xt1=4x/5+4y/5} \atop {yt1+y/3=4x/5+4y/5;}} \right. => \left \{ {{5xt1=4x+4y} \atop {5yt1+5y/3=4x+4y;}} \right. => \left \{ {{t1=\frac{4x+4y}{5x}} \atop {5yt1=4x+7y/3;}} \right. " align="absmiddle" class="latex-formula">
\frac{4x+4y}{5x}=\frac{12x+7y;}{15y} => (4x+4y)15y=(12x+7y)5x " alt="\left \{ {{t1=\frac{4x+4y}{5x}} \atop {t1=\frac{12x+7y;}{15y}}} \right. =>\frac{4x+4y}{5x}=\frac{12x+7y;}{15y} => (4x+4y)15y=(12x+7y)5x " align="absmiddle" class="latex-formula">
12x^2-25xy+12y^2=0;" alt="60xy+60y^2=60x^2+35xy =>12x^2-25xy+12y^2=0;" align="absmiddle" class="latex-formula"> (1)
t1(x-y)=y/3; => 
\frac{4x+4y}{5x}=\frac{y}{3(x-y)} " alt="\left \{ {{t1=\frac{4x+4y}{5x}} \atop {t1=\frac{y}{3(x-y)}} \right. => \frac{4x+4y}{5x}=\frac{y}{3(x-y)} " align="absmiddle" class="latex-formula">
5xy=3(4x+4y)(x-y)=> 5xy=(4x+4y)(3x-3y)=>5xy=12(x*x-y*y)=> 12x*x-5xy-12y*y=0; (2)
(1)+(2):
24x*x-30xy=0 => 24x=30y=> 4xx=5y; => x=5y/4;
t1*5y/4=y(t1+1/3) => 5t1/4=t1+1/3 => 15t1=12t1+4 => 3t1=4 => t1=4/3
Ответ: 4/3 часа