Question

Two pumps can fill a pool tank in 26 hours when working together. Alone, the second pump takes twice as long as the first to fill the tank. How long does it take the first pump alone to fill the tank? ____________________

Answer 1

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,

`V=1=k*d_1*t\\V=1=k*d_2*(2*t)\\==>\ d_1=2*d_2\\\\`

Two pumps can fill a pool tank in 26 hours when working together:

`V=1=k*(d_1+d_2)*26 \ ==> V=1=k*(3*d_2)*26 \ ==>k=(1)/(3*d_2*26) \\\\`

How long does it take the first pump alone to fill the tank:

`V=1=k*d_1*t=k*2*d_2*t=k*3d_2*26\\2*t=3*26\\\\t=(3*26)/(2) \\\\t=3*13\\\\t=39\ (hours)`