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lesantik [10]
3 years ago
15

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 fil

l the tank. How long does it take the first pump alone to fill the tank? ____________________
Mathematics
1 answer:
vesna_86 [32]3 years ago
4 0

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,

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=\dfrac{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=\frac{3*26}{2} \\\\t=3*13\\\\t=39\ (hours)

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