Mathematics question

[Novriil]

Hi!

This is the excersize that was on our olympiade (or whatever I should call it.. like an exam but it shows who are the best in the country):

A scientist wrote a book with an average speed of 6 pages per day. After he had wrote it he still had to copyedit it. Because of that the average speed of the books manifacture dropped to 4,5 pages per day. Find the average speed of copyediting when the number of pages didn't change while copyediting.

Sorry about my english

And thanks if you show all the solving. Not only the answer.

my answer was:

Spoiler

3 pages

but my friend got:

Spoiler

18 pages]

Now am I an idiot or is he?

E: doh I wrote to my answer the wrong number

 

[whauk]

i dont understand it?!

so he writes 6 pages a day and because of the editing process the book only grows 4.5 pages per day?
then he is writing 1.5 pages new every day. is that what you searched for. i am sorry but i cant really follow.

 

[r_517]

1/(1/4.5 - 1/6) = 18 (if my understanding's ok)

suppose the writer wrote x pages in all, and the speed of copyedit is y pages per day.
then he spent: x/6 days in writing the book, then x/y days to copyedit. and after all because the average speed is 4.5pages a day, so he spent x/4.5 days in all.

so that's: x/6 + x/y = x/4.5
y = 1/(1/4.5 - 1/6) = 18

 

[Litz]

If you want the average speed of copyediting for that same book it's 18, but you make it look like you want the average speed of copyediting in order for the book manufacture speed to stay at 6 pages/day, which would be impossible unless you wrote it faster or didn't copyedit at all.

 

[PM 1729]

Hi!

Find the average speed of copyediting
my answer was:

Spoiler

6 pages

but my friend got:

Spoiler

18 pages]

1/(1/4.5 - 1/6) = 18 (if my understanding's ok)

suppose the writer wrote x pages in all, and the speed of copyedit is y pages per day.
then he spent: x/6 days in writing the book, then x/y days to copyedit. and after all because the average speed is 4.5pages a day, so he spent x/4.5 days in all.

so that's: x/6 + x/y = x/4.5
y = 1/(1/4.5 - 1/6) = 18

Your explanation is almost correct but if the speed of editing is more than that of writing, then how can the overall speed decrease?

Spoiler

x/6 +x/y = 2x/4.5
=> y=3.6 pages per day

 

[r_517]

Your explanation is almost correct but if the speed of editing is more than that of writing, then how can the overall speed decrease?

NOTE he said "After he had wrote it he still had to copyedit it." I think he meaned "After he had completed the book."
after all to any writer, the writer should have written down the whole story first, and then modify it. So this writer first wrote the book with the speed of 6 pages per day. After finishing the story, he modified it with the speed of 18 pages per day. So the average speed is decreased to 4.5 pages per day.

 

[PM 1729]

Your explanation is almost correct but if the speed of editing is more than that of writing, then how can the overall speed decrease?

NOTE he said "After he had wrote it he still had to copyedit it." I think he meaned "After he had completed the book."
after all to any writer, the writer should have written down the whole story first, and then modify it. So this writer first wrote the book with the speed of 6 pages per day. After finishing the story, he modified it with the speed of 18 pages per day. So the average speed is decreased to 4.5 pages per day.

Oh..I didn't see that.Yes, then it is 18 pages per day.

 

[Novriil]

damn.. ofcourse. Now I got it. thanks!

 

[amostay2004]

Yes my answer is 18 too.

 

[shelley]

Spoiler

Yay LaTeX!

Okay, so let P = total number of pages, x = number of days to write, y = total number of days (i.e. days to write and copyedit)
\( \frac{P}{x} = 6 \)
\( \frac {P}{y} = 4.5 \)
From this, you know that \( 6x=4.5y \)
You are trying to find average speed of copyediting, where it took y-x days to edit.
\( S = \frac{P}{y-x} \)
Since you know the relation between x and y, solve for one and substitute into this equation.
\( x = \frac{3}{4}y \)
\( S = 4\frac{P}{y} \)
And since you know what \( \frac{P}{y} \) is,
\( S = 4 \times 4.5 = 18 \) pages per day

But of course both of you got it wrong because

Spoiler

you had the wrong units.