Best Answer unreality , 21 July 2007 - 05:19 PM

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# Typists problem

### #11

Posted 12 February 2008 - 09:28 AM

### #12

Posted 12 February 2008 - 06:59 PM

### #13

Posted 13 February 2008 - 09:58 PM

Each typist is only typing 1/2 page per minute. (1 typist x 1/2 page per minute) x 2 minutes will yield 1 page; so to get two pages in two minutes, you need two typists.

Therefore at only 1/2 page per minute, it would take 36 minutes for one typist to finish 18 pages.

### #14

Posted 14 February 2008 - 12:00 AM

If two typists can type two pages in two minutes, how many typists does it take to type 18 pages in 18 minutes?

Assumption: all typists are the same.

Now:

Can each typist type two pages in two minutes? If so, the answer is one, because each typist types one page per minute.

Or, do the two typists type, in total, two pages in two minutes? Then the answer is 2 because every two typists types one page per minute.

### #15

Posted 14 February 2008 - 12:46 AM

### #16

Posted 21 February 2008 - 05:40 PM

So the answer must be 2.

### #17

Posted 27 February 2008 - 09:56 PM

### #18

Posted 01 March 2008 - 11:34 AM

I first heard it posed as ... if a hen and a half can lay an egg and a half in a day and a half, how many hens would it take to lay 18 eggs in 3 days?

It's tempting to figure a hen can lay an egg a day so it would take 6 hens. But it takes a hen and a half to lay an egg a day, so it takes 9 .

In general to solve problems of this type, one can proceed as follows:

Prepare a data table

^ hens eggs days

| 1.5.... 1.5 ....1.5

| x .......18...... 3

Draw an arrow from the unknown x to the known value (in this case of hens). The value of x is then obtained by multiplying the known value by the ratios of the other quantities taken in the same direction of the arrow if they are directly proportional with respect to the unknown x, in the opposite direction if inversely porportional. In this case the number of eggs is directly proportional (more hens, more eggs), the days are inversely proportional (more days, less hens necessary to lay a certain number of eggs).

x = 1.5x(18/1.5)x(1.5/3) = 9.

For the typists problem we have:

^ typists pages minutes

| 2...........2...........2

| x...........18........18

In this case the pages are directly proportional (more typists, more pages), the minutes inversely proportional (more typists, less time to type a certain number of pages). So:

x = 2x(18/2)x(2/18) = 2.

(I couldn't find a better method of drawing the arrow)

### #19

Posted 02 March 2008 - 01:07 AM

**Edited by Ghan3sh, 02 March 2008 - 01:11 AM.**

### #20

Posted 05 March 2008 - 03:57 PM

This question is flawed due to ambiguity. It is missing a word and thus causing confusion. For example:

"If two typists can

**EACH**type two pages in two minutes, how many typists does it take to type 18 pages in 18 minutes?" typing rate per typist is 1 page per minute

Answer - 1 typist

"If two typists

**TOGETHER**can type two pages in two minutes, how many typists does it take to type 18 pages in 18 minutes?" typing rate per typist is 1/2 page per minute

Answer - 2 typists

I believe the question as posed can be reasonably understood as having both meanings, thus clarification is required.

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