Given:
Jena and Matt, working together, can mow the lawn in 4 hours. Working alone, Matt takes four times as long as Jena.
Aim:
We need to find the number of hours Jana takes to mow the lawn alone.
Explanation:
Let x be the number of hours Jana takes to mow the lawn alone.
Given that Working alone, Matt takes four times as long as Jena.
The number of hours Matt takes = 4x.
[tex]\text{ The rate of the working hours are }\frac{1}{x\text{ }}\text{ and }\frac{1}{4x}.[/tex][tex]Combined\text{ rate =}\frac{1}{x}+\frac{1}{4x}[/tex]
[tex]\text{ =}\frac{4}{4x}+\frac{1}{4x}=\frac{4+1}{4x}=\frac{5}{4x}[/tex]
Given that Jena and Matt, working together, can mow the lawn in 4 hours.
[tex]\frac{1}{\frac{5}{4x}}=4[/tex]
[tex]\frac{4x}{5}=4[/tex][tex]x=\frac{5\times4}{4}[/tex][tex]x=5\text{ hours.}[/tex]
Final answer:
Jana takes 5 hours to mow the lawn alone.
