lheiannie07 wrote:George takes 8 hours to copy a 50 page manuscript while Sonya can copy the same in 6 hours. How many hours would it take them to copy a 100 page manuscript, if they work together ?
$$\left(A\right)\ 6\frac{6}{7}$$
B) 9
$$\left(C\right)\ 9\frac{5}{7}$$
$$\left(D\right)\ 10\frac{2}{3}$$
E) 14
The size of the job doubles from 50 pages to 100 pages.
The size of the job can be ANY VALUE, as long as the larger job is double the smaller job.
To make the math easier, let the smaller job = the LCM of the two times = the LCM of 8 and 6 = 24 pages, with the result that the larger job = 2*24 = 48 pages.
Since George takes 8 hours to produce the smaller 24-page job, George's rate = w/t = 24/8 = 3 pages per hour.
Since Sonya takes 6 hours to produce the smaller 24-page job, Sonya's rate = w/t = 24/6 = 4 pages per hour.
Combined rate for George and Sonya = 3+4 = 7 pages per hour.
Since their combined rate is 7 pages per hour, the time for George and Sonya together to produce the larger 48-page job = w/r = 48/7 hours.
The correct answer is
A.
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