Question

A Chinese restaurant has a large goldfish pond. Suppose that an inlet pipe and a hose together can fill the pone in 9 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 aloneThe time that the hose can complete the job alone is______ hour The time that the inlet pipe can complete the job alone is______ hours.

Answer 1

The time that the hose can complete the job alone is 18.513 hour.

The time that the inlet pipe can complete the job alone is 17.513 hours.

Explanation:

Let the number of hours required to fill the pond by hose alone = x

Then the number of hours required to fill the pond by inlet pipe alone = x-1

This means that in 1 hour, the hose alone can fill 1/x of the pond.

Similarly, in 1 hour, the inlet pipe can fill 1/(x-1) if the pond.

Taken together,in 1 hour, the hose and inlet pipe can together fill:

`\[(1)/(x) + (1)/((x-1))\]` of the pond.

But this actually corresponds to 1/9 of the pond.

`\[(1)/(x) + (1)/((x-1)) = (1)/(9)\]`

Solving:

`\[(x-1+x)/(x(x-1)) = (1)/(9)\]`

=>
`\[18x-9 = x^(2)-x\]`

=>
`\[x^(2)-19x+9=0\]`

=> x= 18.513,0.486 ( roots of the quadratic equation)

Of these values, x=18.513 is relevant since x-1 must be non-negative.

So, the number of hours required to fill the pond by hose alone is 18.513 hours

Similarly, the number of hours required to fill the pond by inlet pipe alone is 17.513 hours