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 8 hours to copy a 50 page
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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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
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George's rate is 50/8 = 25/4 and Sonya's rate is 50/6 = 25/3, so their combined rate is: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
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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Thanks a lot!Scott@TargetTestPrep wrote:George's rate is 50/8 = 25/4 and Sonya's rate is 50/6 = 25/3, so their combined rate is: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
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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The size of the job doubles from 50 pages to 100 pages.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 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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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.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
Any doubt ? pl. raise it again.
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