Question

George takes 8 hours to copy a 50 page manuscript while Sonya can copy the same manuscript in 6 hours. How many hours would it take them to copy a 100 page manuscript, if they work together?

• A. $6\frac{6}{7}$
• B. 9
• C. $9\frac{5}{7}$
• D. 14

Answer 1

Answer: (A)

$6\frac{6}{7}$

Answer 2

The correct option is (A): George takes 8 hours to copy a 50 page manuscript
Efficiency of George=$\frac{50}{8}=\frac{25}{4}pages/hr$
Sonya's efficiency= $\frac{50}{6}=\frac{25}{3}pages/hr$
Work done by them working together in 1 hr =$\frac{25}{3}+\frac{25}{4}=\frac{175}{12}$
Time taken when they work together to finish a 100 page manuscript=$100\times\frac{12}{175}=6\frac{6}{7}$hours