Question

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

Answer 1

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:

`\begin{gathered} 4(x+(50)/(3))=100 \\ x+(50)/(3)=(100)/(4) \\ x=25-(50)/(3) \\ x=(25)/(3) \end{gathered}`

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

`(100)/(x)=(100)/((25)/(3))=(100\cdot3)/(25)=12`