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Diana can type 100 form lettersin six hours. When Frankie helps,they can do the job in four hours.How long would it take Frankie todo this job alone?[?] hours

Sagot :

Let x be the number of form letters which Frankie can type in an hour.

We know that Diana can type 100/6 = 50/3 form letters in a hour.

Since they can type 100 letters together in four hours, we have:

[tex]\begin{gathered} 4(x+\frac{50}{3})=100 \\ x+\frac{50}{3}=\frac{100}{4} \\ x=25-\frac{50}{3} \\ x=\frac{25}{3} \end{gathered}[/tex]

Therefore, the number of hours needed to Frankie do this job alone is given by:

[tex]\frac{100}{x}=\frac{100}{\frac{25}{3}}=\frac{100\cdot3}{25}=12[/tex]