SOLUTION: Ron and hermoine type papers for other students to pay for college. On Saturday, they worked 6 hours each an typed a total of 198 pages. On Sunday, Hermoine worked for 2 hours befo

Question 390295: Ron and hermoine type papers for other students to pay for college. On Saturday, they worked 6 hours each an typed a total of 198 pages. On Sunday, Hermoine worked for 2 hours before Ron could join her. Together, they worked another 5 hours and typed a total of 201 pages. How many hours will it take Hermoine to type a 27 page paper if she works alon?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!

Let x=amount of time it will take Hermoine working alone to type 27 pages
Then Hermoine works at the rate of 27/x pages per hour
Together Ron and Hermoine types at the rate of 198/6 =33 pages per hour
Hermoine working alone for 2 hours typed (27/x)*2=54/x pages
When Ron joined, together, they worked for 5 hours and typed (201-54/x)pages
So together, they worked at the rate of ((201-54/x))/5 pages per hour
So, our equation to solve is:
((201-54/x))/5=33
201-54/x=165
201x-54=165x
36x=54
x=1.5 hours---time it takes hermoine working alone to type 27 pages
Therefore Hermoine types at the rate of 27/1.5=18 pages per hour
CK
In 2 hours, Hermoine types 2*18= 36 pages leaving 201-36=165 pages for both to complete
In 5 hours Ron and Hermoine working together types 33*5=165 pages
165=165
Hope this helps---ptaylor

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