Question

Save & Exit Certify Lesson: 5.5 Applications involving Rational ..DONALD VANSICKLEQuestion 3 of 10, Step 1 of 11/10CorrectJena and Matt, working together, can mow the lawn in 4 hours. Working alone, Matt takes four times as long as jena. How long does it take Jena to mow the lawn alone?AnswerKeypadKeyboard Shortcutshours

Answer 1

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.

Step-by-step 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.

`\text{ The rate of the working hours are }\frac{1}{x\text{ }}\text{ and }(1)/(4x).`
`Combined\text{ rate =}(1)/(x)+(1)/(4x)`

`\text{ =}(4)/(4x)+(1)/(4x)=(4+1)/(4x)=(5)/(4x)`

Given that Jena and Matt, working together, can mow the lawn in 4 hours.

`(1)/((5)/(4x))=4`

`(4x)/(5)=4`
`x=(5*4)/(4)`
`x=5\text{ hours.}`

Final answer:

Jana takes 5 hours to mow the lawn alone.