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# George takes 8 hours to copy a 50 page manuscript while Sonya can copy

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Math Expert
Joined: 02 Sep 2009
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George takes 8 hours to copy a 50 page manuscript while Sonya can copy  [#permalink]

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29 Jun 2017, 11:56
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Difficulty:

15% (low)

Question Stats:

86% (01:54) correct 14% (02:10) wrong based on 87 sessions

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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 ?

A) $$6\frac{6}{7}$$

B) 9

C) $$9\frac{5}{7}$$

D) $$10\frac{2}{3}$$

E) 14

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George takes 8 hours to copy a 50 page manuscript while Sonya can copy  [#permalink]

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29 Jun 2017, 12:09
To make things easy the work done to copy a 50 page manuscript is 48 units.
So George does 6 units/hour, where as Sonya does 8 units/hour

Since they have to copy a 100 page manuscript, it would take them 96 units of work
At their combined rates(14 units/hour) it will take them $$\frac{96}{14}$$
= $$\frac{48}{7}$$ =$$6\frac{6}{7}$$(Option A)
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Re: George takes 8 hours to copy a 50 page manuscript while Sonya can copy  [#permalink]

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29 Jun 2017, 12:36
2
Bunuel 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 ?

A) $$6\frac{6}{7}$$

B) 9

C) $$9\frac{5}{7}$$

D) $$10\frac{2}{3}$$

E) 14

George takes 8 hours to copy 50 page. His per hour work $$= \frac{1}{8}$$

Sonya takes 6 hours to copy 50 page. Her per hour work $$= \frac{1}{6}$$

Per hour work of George and Sonya together $$= \frac{1}{8} + \frac{1}{6} = \frac{3 + 4}{24} = \frac{7}{24}$$

Time taken to copy 50 pages by both George and Sonya together $$= \frac{24}{7}$$

To copy 100 pages will take twice the time to copy 50 pages.

Therefore Time to copy 100 pages by both George and Sonya together $$= \frac{24}{7} *2 = \frac{48}{7} = 6 \frac{6}{7}$$

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Re: George takes 8 hours to copy a 50 page manuscript while Sonya can copy  [#permalink]

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29 Jun 2017, 12:49
pushpitkc wrote:
To make things easy the work done to copy a 50 page manuscript is 48 units.
So George does 6 units/hour, where as Sonya does 8 units/hour

Since they have to copy a 100 page manuscript, it would take them 96 units of work
At their combined rates(14 units/hour) it will take them $$\frac{96}{14}$$
= $$\frac{48}{7}$$ =$$6\frac{6}{7}$$(Option A)

pushpitkc
can you elaborate your solution! it is interesting! and easier than the conventional one.
thanks
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Re: George takes 8 hours to copy a 50 page manuscript while Sonya can copy  [#permalink]

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02 Jul 2017, 04:52
Time taken by both together to copy 50 page manuscript

1/8 + 1/6 = 1/T

Total work is two units (100 pages) - total time is 48/7 or Option A
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George takes 8 hours to copy a 50 page manuscript while Sonya can copy  [#permalink]

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02 Jul 2017, 05:58
Posting my way of solving rate problems..
Please rate the way of my solution..

given in the question,
George takes 8 hours to copy a 50 page manuscript
so rate(G) = 50/8 [rate=work done/time]
also given in the question,
Sonya can copy the same in 6 hours
so rate(S) = 50/6

Working together--
rate(G)+rate(S)= 50/8 + 50/6 = 25x7/12 [multiplication of the numbers are not required it will help in simplification in last step]

So time taken by both working together to copy 100 pages = 100/ rate(G) + rate(S) = 100x12/25x7 = 48/7 [A]

Thanks in advance for the Kudos I will recieve.......
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George takes 8 hours to copy a 50 page manuscript while Sonya can copy  [#permalink]

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02 Jul 2017, 11:02
Bunuel 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 ?

A) $$6\frac{6}{7}$$

B) 9

C) $$9\frac{5}{7}$$

D) $$10\frac{2}{3}$$

E) 14

These numbers aren't as hard as they looked for the standard method.

1. Find rates in $$\frac{pages}{hour}$$

George's rate = $$\frac{50}{8}$$ and Sonya's rate = $$\frac{50}{6}$$. Simplify both rates to $$\frac{25}{4}$$ and $$\frac{25}{3}$$

2. They work together; combine the rates using LCD 12, where George = $$\frac{75}{12}$$ and Sonya = $$\frac{100}{12}$$

Combined rate: $$\frac{75}{12}$$ + $$\frac{100}{12}$$ = $$\frac{175}{12}$$

Work is 100 pages. Combined rate is $$\frac{175}{12}$$

3. $$\frac{W}{r}$$= t. --------> $$\frac{100}{(\frac{175}{12})}$$ =

$$100 *\frac{12}{175}$$ ------> factor out 25:

(4 * $$\frac{12}{7}$$) = $$\frac{48}{7}$$ =

6$$\frac{6}{7}$$

sashiim20
From 50 pages/8 hours and 50 pages/6 hours, I cannot understand how you got rates for George and Sonya, respectively, of $$\frac{1}{8}$$ and $$\frac{1}{6}$$. It can't be pages per hour, obviously. How did you arrive at these calculations?
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Re: George takes 8 hours to copy a 50 page manuscript while Sonya can copy  [#permalink]

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02 Jul 2017, 12:29
Bunuel 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 ?

A) $$6\frac{6}{7}$$

B) 9

C) $$9\frac{5}{7}$$

D) $$10\frac{2}{3}$$

E) 14

h*7/24=2
h=6 6/7 hours
Re: George takes 8 hours to copy a 50 page manuscript while Sonya can copy   [#permalink] 02 Jul 2017, 12:29
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