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
[tex]Rate=\frac{Volume\text{ }}{Time}[/tex]
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
[tex]Rate=\frac{1}{20}[/tex]
The rate at which Jordan can replace an engine alone is
[tex]Rate=\frac{1}{k}[/tex]
The rate at which both of them can replace an engine is
[tex]Rate=\frac{1}{6}[/tex]
Total work rate is
[tex]\frac{1}{20}+\frac{1}{k}=\frac{1}{6}[/tex]
Solve to find k,
[tex]\begin{gathered} Collect\text{ like terms} \\ \frac{1}{k}=\frac{1}{6}-\frac{1}{20} \\ \frac{1}{k}=\frac{10-3}{60}=\frac{7}{60} \\ \frac{1}{k}=\frac{7}{60} \\ k=\frac{60}{7} \\ k=8.571428571\text{ hours} \\ k=8.6\text{ hours (1 decimal place)} \end{gathered}[/tex]
Hence, it will take Jordan 8.6 hours (1 decimal place) to replace an engine alone.
