Respuesta :
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,
[tex]\text{ }\frac{1}{5x}\text{ + }\frac{1}{x}\text{ = }\frac{1}{5}[/tex][tex]\text{ }\frac{x}{5x^2}\text{ + }\frac{5x}{5x^2}\text{ = }\frac{1}{5}[/tex][tex]\text{ }\frac{\text{ 6x}}{5x^2}\text{ = }\frac{1}{5}[/tex][tex]\text{ (6x)(5) = (1)(5x}^2)[/tex][tex]\text{ 30x = 5x}^2[/tex][tex]\text{ }\frac{\text{30x}}{5\text{x}}\text{ = }\frac{5\text{x}^2}{5\text{x}}[/tex][tex]\text{ 6 = x}[/tex]Therefore, it'll take Jenna 6 hours to rake the yard alone.
