INVERSE VARIATION
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» Solve the given:
- Let (p) be the number of people
- Let (h) be the hours taken
[tex] \: : \implies \sf \large p = \frac{k}{h} \\ [/tex]
[tex]\large \tt \red{given} \begin{cases} \sf \: p = 5 \\ \sf \: h = 5\end{cases}[/tex]
» Substitute to find the constant (k).
[tex]\implies \sf \large 5 = \frac{k}{5} \\ [/tex]
[tex]\implies \sf \large 5 \times 5 = \frac{k}{ \cancel5} \times \cancel5 \\ [/tex]
[tex]\implies \sf \large 25 = k[/tex]
[tex]\implies \sf \large k = 25[/tex]
» Now find how much hours will it take for two people to work.
[tex]\large \tt \red{given} \begin{cases} \sf \: p = 2 \\ \sf \: k = 25\end{cases}[/tex]
[tex] \implies \sf \large 2 = \frac{25}{h} \\ [/tex]
[tex] \implies \sf \large 2 \times h = \frac{25}{ \cancel{h}} \times \cancel{h} \\ [/tex]
[tex] \implies \sf \large 2h = 25[/tex]
[tex] \implies \sf \large \frac{ \cancel2h}{ \cancel2} = \frac{25}{2} \\ [/tex]
[tex] \implies \sf \large h = 12 \frac{1}{2} [/tex]
[tex] \: [/tex]
Final Answer:
[tex] \tt \huge» \: \purple{12 \frac{1}{2} \: \: hours}[/tex]
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