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Three secretaries working together can type 36 pages of text in half

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Bunuel
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Three secretaries working together can type 36 pages of text in half [#permalink] New post   19 Jan 2021, 01:11
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Three secretaries working together can type 36 pages of text in half an hour. If the typing speeds of the secretaries are in a 4:3:2 ratio, how long will it take the slowest-typing secretary working alone to type 52 pages of text?

A. 1 hour and 34 minutes
B. 1 hour and 45 minutes
C. 2 hours and 24 minutes
D. 3 hours and 15 minutes
E. 3 hours and 25 minutes


M37-63

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D
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rocky620
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Re: Three secretaries working together can type 36 pages of text in half [#permalink] New post   19 Jan 2021, 05:32
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Since the all three type 36 pages in 30 minutes, with the speed ratio of 4:3:2. Individually they will type
Sec-1 = \(\frac{36}{9}\)*4 = 16

Sec-2 = \(\frac{36}{9}\)*3 = 12

Sec-3 = \(\frac{36}{9}\)*2 = 8

The slowest Sec is typing 8 pages in 30 mins.
So, she will type 52 pages in : \(\frac{30}{8}\)*52 = 195 mins = 3 hours and 15 minutes

Option D
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Re: Three secretaries working together can type 36 pages of text in half [#permalink] New post   19 Jan 2021, 08:57
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Given, 3 secretaries in 1 hr type 72 pages

Ratio = 4:3:2, Let multiplier factor = x
9x= 72, x= 8. So, slowest secretary type = 2x= 16 pages in 1 hr.
Now, slowest secretary type 52 pages in 52/16 hrs. = 3 hr 15 mins

So, I think D. :)
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Re: Three secretaries working together can type 36 pages of text in half [#permalink] New post   19 Jan 2021, 13:11
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Since we have been given the ratio of the typing speeds of the secretary => 4:3:2 and that they type 36 pages in \(\frac{1}{2}\) an hour, it will be easy to find out how many pages did they individually type in \(\frac{1}{2}\) hour.

Secretary 1= \(\frac{36*4}{9}\) = 16 pages || Secretary 2 = \(\frac{36*3}{9}\) = 12 pages || Secretary 3= \(\frac{36*2}{9}\) = 8 pages.

Therefore, if Secretary 3 takes \(\frac{1}{2}\) an hour to type 8 pages, to type 52 pages she will take \(\frac{52}{16}\)= 3 hours and 15 minutes.

The OA is D.
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Re: Three secretaries working together can type 36 pages of text in half [#permalink] New post   30 Nov 2021, 03:25
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Three secretaries working together can type 36 pages of text in half an hour. If the typing speeds of the secretaries are in a \(4:3:2\) ratio, how long will it take the slowest-typing secretary working alone to type 52 pages of text?

A. 1 hour and 34 minutes
B. 1 hour and 45 minutes
C. 2 hours and 24 minutes
D. 3 hours and 15 minutes
E. 3 hours and 25 minutes


In half an hour the slowest-typing secretary types \(\frac{2}{4+3+2}=\frac{2}{9}\)th of 36 pages, so 8 pages in half an hour. In an hour the secretary will type 16 pages, so to type 52 pages, \(\frac{52}{16}=3\frac{1}{4}\) hours, or 3 hours and 15 minutes is needed.


Answer: D
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Re: Three secretaries working together can type 36 pages of text in half [#permalink] New post   17 Apr 2023, 12:32
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Three secretaries working together can type 36 pages of text in half an hour. If the typing speeds of the secretaries are in a 4:3:2 ratio, how long will it take the slowest-typing secretary working alone to type 52 pages of text?
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Re: Three secretaries working together can type 36 pages of text in half [#permalink]
17 Apr 2023, 12:32
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