Question

A Chinese restaurant has a large goldfish pond. Suppose that an inlet pipe and a hose together can fill the pond in 2 hours. The inlet pipe alone can complete the job in one hour less time than the hose alone. Find the time that the hose can complete the job alone and the time that the inlet pipe can complete the job alone. The time that the hose can complete the job alone is nothing hours. ​(Round to the nearest​ tenth.)

Answer 1

Answer:

Therefore The inlet pipe can fill the pond in 3.57 hours

and the hose can fill the pond in (3.57+1)=4.57 hours.

Step-by-step explanation:

Let, The inlet pipe fill the goldfish pond in x hours

So the hose fill the goldfish pond in (x+1) hours.

Then inlet pipe fill  $\frac{1}{x}$ parts of the pond in 1 hour.

And the hose filled $\frac{1}{1+x}$ parts of the pond in 1 hour.

In 1 hour the two pipes filled $(\frac{1}{x}+\frac{1}{x+1})$ parts of the pond

                                            $=\frac{x+1+x}{x(x+1)}$ parts

                                            $=\frac{2x+1}{x^2+x}$ parts

Given that The inlet pipe and hose together can fill the pond in 2 hour.

Then , in 2 hour the two pipes filled $=2(\frac{2x+1}{x^2+x})$ parts of the pond.

The pond is 1 part.

According to the problem,

$2(\frac{2x+1}{x^2+x})=1$

$\Rightarrow 2(2x+1)=x^2+x$

$\Rightarrow x^2+x=4x+2$

⇒x²+x-4x-2=0

⇒x²-3x-2=0

$\Rightarrow x=\frac{-(-3)\pm\sqrt{(-3)^2-4.1(-2)}}{2.1}$

       $=\frac{3\pm\sqrt{17}}{2}$

       =3.56,-0.561

Since time can't negative.

Then x =3.57 hours.

Therefore The inlet pipe can fill the pond in 3.57 hours

and the hose can fill the pond in (3.57+1)=4.57 hours.