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

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

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New post 29 Jun 2017, 11:56
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Question Stats:

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

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New post 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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New post 29 Jun 2017, 12:36
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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 \(= \frac{24}{7} *2 = \frac{48}{7} = 6 \frac{6}{7}\)

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

1/8 + 1/6 = 1/T
T = 24/7

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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New post 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....... :-D :-D :-D :-D :-D
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George takes 8 hours to copy a 50 page manuscript while Sonya can copy  [#permalink]

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New post 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\(\frac{6}{7}\)

Answer A


sashiim20
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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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New post 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
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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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