Question

hunter can replace an engine by himself in 20 hours. with the help of jordan they can both replace it in 6 hours, how long does it take for jordan to replace it on his own ? round to the nearest hundred

Answer 1

Mr Hunter can replace an engine in 20 hours

Let the time taken for Jordan to replace an engine be represented by k

The both of them can replace the engine in 6 hours

The formula for work rate is

`Rate=\frac{Volume\text{ }}{Time}`

Since they are replacing an engine, let the volume be represented by 1

The rate at which Mr Hunter can replace an engine alone is

`Rate=(1)/(20)`

The rate at which Jordan can replace an engine alone is

`Rate=(1)/(k)`

The rate at which both of them can replace an engine is

`Rate=(1)/(6)`

Total work rate is

`(1)/(20)+(1)/(k)=(1)/(6)`

Solve to find k,

`\begin{gathered} Collect\text{ like terms} \\ (1)/(k)=(1)/(6)-(1)/(20) \\ (1)/(k)=(10-3)/(60)=(7)/(60) \\ (1)/(k)=(7)/(60) \\ k=(60)/(7) \\ k=8.571428571\text{ hours} \\ k=8.6\text{ hours (1 decimal place)} \end{gathered}`

Hence, it will take Jordan 8.6 hours (1 decimal place) to replace an engine alone.