Question

Jenna and Cara , working together, can rake the yard in 5 hours. Working alone, cara text five times as long as Jenna. How long does it take Jenna to rake the yard alone?

Answer 1

Given:

a.) Jenna and Cara, working together, can rake the yard in 5 hours.

b.) Working alone, Cara text five times as long as Jenna.

Let,

Time taken if Cara work alone = 5x

Time taken if Jenna work alone = x

We get,

`\text{ }(1)/(5x)\text{ + }(1)/(x)\text{ = }(1)/(5)`
`\text{ }(x)/(5x^2)\text{ + }(5x)/(5x^2)\text{ = }(1)/(5)`
`\text{ }\frac{\text{ 6x}}{5x^2}\text{ = }(1)/(5)`
`\text{ (6x)(5) = (1)(5x}^2)`
`\text{ 30x = 5x}^2`
`\text{ }\frac{\text{30x}}{5\text{x}}\text{ = }\frac{5\text{x}^2}{5\text{x}}`
`\text{ 6 = x}`

Therefore, it'll take Jenna 6 hours to rake the yard alone.