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Sagot :
We know that
• Emma can dig a 13 ft by 6 ft hole in 8.5 hours.
,• Kennedy can dig the same hole in 14 hours.
We are going to express the "hole" as unit 1 since both of them did one. The following rates express the job done for each person.
• Emma rate = 1/8.5 (job per hour)
,• Kennedy rate = 1/14 (job per hour).
,• The rate where they work together is 1/x.
Now, we form the equation with those rates
[tex]\frac{1}{x}=\frac{1}{8.5}+\frac{1}{14}[/tex]Then, we solve for x, we sum the fractions first
[tex]\begin{gathered} \frac{1}{x}=\frac{14+8.5}{119} \\ \frac{1}{x}=\frac{22.5}{119} \end{gathered}[/tex]Now, we multiply in cross form
[tex]\begin{gathered} 1\cdot119=22.5\cdot x \\ 22.5x=119 \end{gathered}[/tex]Then, we divide the equation by 22.5
[tex]\begin{gathered} \frac{22.5x}{22.5}=\frac{119}{22.5} \\ x\approx5.29 \end{gathered}[/tex]Therefore, if they work together, they will finish the hole in 5 hours approximately.
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