Respuesta :
Let x be the time in which Jesse can mow the lawn, this means that in one hour she mows:
[tex]\frac{1}{x}[/tex]of the lawn in one hour
Now, we know that Norton mows tha lawn in 4 hours, that means that he mows
[tex]\frac{1}{4}[/tex]of the lawn in one hour.
Now, since when they work together they spent 2.5 hours this means that:
[tex]\frac{1}{x}+\frac{1}{4}=\frac{1}{2.5}[/tex]Now, solving for x we have:
[tex]\begin{gathered} \frac{1}{x}+\frac{1}{4}=\frac{1}{2.5} \\ \frac{4+x}{4x}=\frac{1}{2.5} \\ x+4=\frac{4x}{\frac{25}{10}} \\ x+4=\frac{40}{25}x \\ x+4=\frac{8}{5}x \\ \frac{8}{5}x-x=4 \\ \frac{3}{5}x=4 \\ x=\frac{4}{\frac{3}{5}} \\ x=\frac{20}{3} \end{gathered}[/tex]Therefore Jesse mows the lawn in 20/3 hours (this is, rounded to the hundreths, 6.67 hours.)
