Respuesta :

Answer:

45 minutes

Step-by-step explanation:

It is given that one hose can fill a goldfish pond in 36 minute

So the the first hose can fill goldfish pond [tex]\frac{1}{36}[/tex] per minute

When both fill together then they fill in 20 minutes

So the the both  hose can fill goldfish pond [tex]\frac{1}{20}[/tex] per minute

Let Goldfish pond filled by second hose  [tex]\frac{1}{x}[/tex] per minute

so [tex]\frac{1}{36}+\frac{1}{x}=\frac{1}{20}[/tex]

[tex]\frac{1}{x}=\frac{1}{20}-\frac{1}{36}[/tex]

x=45 minutes

Answer:

The time taken by the second hose alone to fill the pond is 45 minutes.

Step-by-step explanation:

One hose can fill a goldfish pond in 36 ​minutes.

Let second hose can fill the pond alone in x minutes.

The part of goldfish pond filled by one hose in 1 minute is [tex]\frac{1}{36}[/tex].

The part of goldfish pond filled by second hose in 1 minute is [tex]\frac{1}{x}[/tex].

Two hoses can fill the same pond in 20 minutes.

The part of goldfish pond filled by both hose in 1 minute is [tex]\frac{1}{20}[/tex].

[tex]\frac{1}{36}+\frac{1}{x}=\frac{1}{20}[/tex]

[tex]\frac{x+36}{36x}=\frac{1}{20}[/tex]

[tex]20(x+36)=36x[/tex]

[tex]20x+720=36x[/tex]

[tex]720=36x-20x[/tex]

[tex]720=16x[/tex]

[tex]\frac{720}{16}=x[/tex]

[tex]45=x[/tex]

Therefore, the time taken by the second hose alone to fill the pond is 45 minutes.