Respuesta :
Imani picked up 40 bushels of apple in 8.2 hours.
And Chelsea picked up 40 bushels of apple in 10.8 hours
Let I be Imani ratio, hence we have
[tex]I=\frac{40}{8.2}[/tex]and let C be Chelsea ratio, hence,
[tex]C=\frac{40}{10.8}[/tex]Now, let T be the ratio when Chelsea and Imani work together. In this case, we have
[tex]T=\frac{40}{t}[/tex]where t is the time for their work.
This means that,
[tex]I+C=T[/tex]that is, this equality must be fulfilled in order to compare both cases. Hence,
[tex]\frac{40}{8.2}+\frac{40}{10.8}=\frac{40}{t}[/tex]we can factorize 40 in both sides, hence, we have that
[tex]\frac{1}{8.2}+\frac{1}{10.8}=\frac{1}{t}[/tex]Now, we must solve this equality for t. Therefore, we have
[tex]\frac{10.8+8.2}{(10.8)(8.2)}=\frac{1}{t}[/tex]or
[tex]\frac{19}{88.56}=\frac{1}{t}[/tex]it yields,
[tex]0.2145=\frac{1}{t}[/tex]Finally, t is equal to
[tex]\begin{gathered} t=\frac{1}{0.2145} \\ t=4.66 \end{gathered}[/tex]that is, of they work together, they will take 4.66 hours only
