Question

е A Chinese restaurant has a large goldfish pond. Suppose that an inlet pipe and a hose together can fill the pond in 3 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. ntents Library The time that the hose can complete the job alone is (?) hours. (Round to the nearest tenth.) The time that the inlet pipe can complete the job alone is (? )hours. (Round to the nearest tenth.) nizer

Answer 1

Let the time for the pipe to complete the Job be represented as

`p`

Let the time for the hose to complete the Job be represented as

`h`

The pipe and the hose completed the job in 3hours

Hence we have the equation

`p+h=3`

The inlet pipe alone can complete the job in one hour less time than the hose alone implies that

`h-p=1`

This leads to a system of equation which we now solve simultaneously

`\begin{gathered} h+p=3\ldots\text{.eq}1 \\ h-p=1\ldots\text{.}\mathrm{}eq2 \end{gathered}`

Adding eq1 and eq2, we o btain

`\begin{gathered} 2h=4 \\ h=(4)/(2)=2 \end{gathered}`

Substituting the value of h into eq1 we have

`\begin{gathered} h+p=3 \\ 2+p=3 \\ p=3-2 \\ p=1 \end{gathered}`

Therefore

`h=2,\text{ p=1}`

The time that the inlet pipe can complete the job alone is 1 hours

The time that the hose can complete the job alone is 2 hours