Answer:
Step-by-step explanation:
Let's say
d1 the outflow of the first pump
d2 the outflow of the second pump
V=1 is the volume of the tank
Since the second pump takes twice as long as the first to fill the tank,
[tex]V=1=k*d_1*t\\V=1=k*d_2*(2*t)\\==>\ d_1=2*d_2\\\\[/tex]
Two pumps can fill a pool tank in 26 hours when working together:
[tex]V=1=k*(d_1+d_2)*26 \ ==> V=1=k*(3*d_2)*26 \ ==>k=\dfrac{1}{3*d_2*26} \\\\[/tex]
How long does it take the first pump alone to fill the tank:
[tex]V=1=k*d_1*t=k*2*d_2*t=k*3d_2*26\\2*t=3*26\\\\t=\frac{3*26}{2} \\\\t=3*13\\\\t=39\ (hours)[/tex]
