George takes 8 hours to copy a 50 page

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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

How will i start solving it? Can some experts help me on this?

OA A

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by [email protected] » Mon Oct 16, 2017 3:39 pm
Hi leiannie07,

This is an example of a "Work Formula" question - when you have two entities working together on a task, you can use the following formula to determine how long it will take the two entities to complete the task:

(A)(B)/(A+B) = time to complete the task (where A and B are the two times it takes the individuals to complete the task when working alone)

We're told that George takes 8 hours to copy a 50 page manuscript and Sonya can copy the same 50 page manuscript in 6 hours. We're asked how long it would take them to complete a 100-page manuscript when working together, so we have to think in those terms...

George = 16 hours to complete 100 pages
Sonya = 12 hours to complete 100 pages

(16)(12)/(16+12) =
192/28 =
6 24/28 =
6 6/7 hours

Final Answer: A

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by Scott@TargetTestPrep » Sun Oct 22, 2017 3:49 pm
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
George's rate is 50/8 = 25/4 and Sonya's rate is 50/6 = 25/3, so their combined rate is:

25/4 + 25/3 = 75/12 + 100/12 = 175/12.

Thus, it will take them 100/(175/12) = (100 x 12)/175 = (4 x 12)/7 = 48/7 = 6 6/7 hours.

Answer: A

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by BTGmoderatorDC » Wed Jan 10, 2018 12:45 am
Scott@TargetTestPrep wrote:
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
George's rate is 50/8 = 25/4 and Sonya's rate is 50/6 = 25/3, so their combined rate is:

25/4 + 25/3 = 75/12 + 100/12 = 175/12.

Thus, it will take them 100/(175/12) = (100 x 12)/175 = (4 x 12)/7 = 48/7 = 6 6/7 hours.

Answer: A
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by GMATGuruNY » Wed Jan 10, 2018 5:13 am
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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by GMATWisdom » Wed Jan 10, 2018 11:29 am
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

How will i start solving it? Can some experts help me on this?

OA A
George takes eight 8 hours to copy a 50 page manuscript. If Sonya also takes 8 hours to copy the 50 page manuscript then together they would finish 100 page manuscript in 8 hours. But Sonya copies faster than George because she takes only 6 hours to copy the 50 page manuscript therefore together they will copy the 100 page manuscript in less than eight hours. Since there is only one option A which is less than 8 hours hence option A must be correct.
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