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Sagot :
c = Hours it take Cindy by herself
p =Hours it take Pam by herself
now, we know if they work together, they can finish in 10 hours, so let's take a peek at their rate.
whilst working together
in 1 hr Cindy has done 1/c "th" of the whole work
in 1 hr Pam has done 1/p "th" of the whole work
and since we know the whole work's time is 10 hours, in 1 hour they both have done 1/10 of whole lot, so
[tex]\stackrel{\textit{Cindy's rate}}{\cfrac{1}{c}}+\stackrel{\textit{Pam's rate}}{\cfrac{1}{p}}=\stackrel{\textit{fraction of total work}}{\cfrac{1}{10}}~\hfill \stackrel{\textit{since Pam takes 5 times longer}}{p=5c} \\\\\\ \cfrac{1}{c}+\cfrac{1}{5c}=\cfrac{1}{10}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{10c}}{10c\left( \cfrac{1}{c}+\cfrac{1}{5c} \right)=10c\left( \cfrac{1}{10} \right)}\implies 10+2=c\implies \stackrel{hours}{12=c}[/tex]
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