Typing trouble?

Let the total no. of pages in the manuscript be 'x'

In the 1st half of the typing, the typing speed is 10 pages per day. Therefore, 10 pages are typed in 1 day Therefore, half the document, i.e., (x/2)pages are typed in : (1/10) X (x/2) days = x/20 days.

In the 2nd half of the typing, the typing speed is 30 pages per day. Therefore, 30 pages are typed in 1 day Therefore,the remaining half of the document, i.e., (x/2)pages are typed in : (1/30) X (x/2) days = x/60 days.

Thus, total no. of pages typed = x Total time taken = (x/20) + (x/60) = (4x)/(60) = x/15

Thus typing average = (Total no. of pages typed) / (Total time taken) = (x)/(x/15) = 15

Thus the average speed is 15 pages per day.

Typing 30 pages per day takes 3 times as less time than typing 10 pages per day. The daughter actually typed an average of 15 pages per day, so the mother is right. (Both can't be right at the same time and both can't be wrong at the same time because the two are opposites. I don't know why those answers were there. Maybe there was nothing else to put?).

Let me better explain this with a problem of Time Speed distance, If u go the first half n hr at a 10Km/Hr and the rem. half at 30Km/Hr then the avg. speed should be 10*30/(10+30) = 7.5Kmph. Same is the case of above

daughter is taking almost the same time (only during typing@10 a day), which is required to finish the whole work (if she is typing @20 a day). Hence the time taken by daughter during @ 30 a day is extra.

$\text{Let the total no. of pages in the manuscript be 'x' In the 1st half of the typing, the typing speed is 10 pages per day. Therefore, 10 pages are typed in 1 day Therefore, half the document, i.e., (x/2)pages are typed in : (1/10) X (x/2) days = x/20 days. In the 2nd half of the typing, the typing speed is 30 pages per day. Therefore, 30 pages are typed in 1 day Therefore,the remaining half of the document, i.e., (x/2)pages are typed in : (1/30) X (x/2) days = x/60 days. Thus, total no. of pages typed = x Total time taken = (x/20) + (x/60) = (4x)/(60) = x/15 Thus typing average = (Total no. of pages typed) / (Total time taken) = (x)/(x/15) = 15 Thus the average speed is 15 pages per day.}$

Ok as the girl said her mother that she will complete her work at speed of 20 pages/day. she actually did half by

10 pages/day and half by 30 pages/day if you take mean of it it comes to be 20 but remember mean is not always average

when it comes to finding slope of something. By definition mean is (total y quantity)/(total x quantity){in this case is number of pages and x is number of days}.

Since we don't know any one lets assume no of pages to be 300 {as it is a multiple of all the given rates or slopes}

then number days while doing 150 pages of work at 10 p/day comes to be 15 , Similarly for

20 p/days comes out to be 5 calculating the average slope = (150+150)/(5+15) = 15 not 20. So her mother was correct.

take the LCM of 10 , 20 and 30 i.e. 60 Number of days she worked : For 60 pages : half of the pages = 30 pages 10 pages a day for 30 pages = 3 days 30 pages a day for 30 pages =1 day total number of days she worked = 4 days Number of days she claimed: 20 pages for 60 days = 3 days so her claim is wrong and her mother was right.

Mother is right. Because, for example , 100 pages manuscript can be completed, in five days if the daughter keeps her speed @ 20 pp or more per day but if she starts at the speed of 10 pp per day she would obviously finish only half after 5th day i.e. 50 pp only.Since the No. of pages of the manuscript is not known , the mother is quite right. Daughter's perception is correct, if the number of pages of the manuscript is 40, 80 or 120 etc in the instant case.

let no. of pages be x .. so the no. of days is supposed to be >> x/20

but ,, she wrote x/2 pages with rate 10 pages per day therefore, the no. of days needed to finish only the first half equals >> x/20

similarly ,, no. of days needed to finish the second half equals >> x/60 so the total days will never be equal to what it was supposed to be.

Mothers are always right !! xDD

She types half of the document at half rate expected. And thus, utilizes total expected time to complete just half the document. Rest whatever amount of time it takes is over the expected time. And hence, mother was correct.

Let the number of pages be 120. First half = 60 pages in 6 days at 10 per day. rest 60 in two days. Total days = 8. Avg= 20/day should have been 140 pages .

Let the full length of the manuscript be 200 pages. The daughter's claim can be re-structured thus to "I will finish typing the manuscript in 10 days." According to the lemma, she typed the first half of the manuscript in (200/2)/10=10 days. Clearly, she didn't average 20 pages a day.

consider the question taken from the concept of speed, distance and time. let there be x no. of pages. For first half, no. of pages=x/2 and speed=10 pages a day so no. of days taken=no. of pages/speed which comes.out to be x/20. similarly no. of days taken for second half=x/60. total no. of days taken=x/20 + x/60 which is x/15. Now average speed =total no. of pages/no. of days taken i.e. x/x/15 = 15. implies mother is correct

let total pages to be typed=X total days required,if typed 20 pages/day=X/20 total days required,if typed half 10pages/day and other half 30pages/day=(X/10)+(X/30)=X/15

BOTH ARE NOT EQUAL

Average speed : 2xy/x+y = 2.10.30/10+30 = 15 pages/ day therefore, the MOTHER is correct!

Let's assume that the total number of pages is 60, so that she will do the 2nd half in one day.

The first half, which is the other 30 pages, is done 10 pages a day. $30/10 = 3 days$ .

From there we can say that she did the whole manuscript for 4 days.

$60 / 4 = \boxed{15}$ pages per day

lets assume the number of pages in the manuscripts were 60x pages (for simple calculation). The daughter said she will type at an average of 20 pages/day.

The daughter typed

-first half: @ 10 pages per day i.e 30x script took her 3x days

-next half @ 30 pages per day: i.e 30x script took her x days

total days = 4x days

which means: 60x/4x= 15 pages/day

assume there are 40 pages... first half read in 2 days and other half in 20/30 days. total days= 2+.66=2.66 Average= 40/2.66 which is not equal to 20.

A simple example should suffice here. Lets say there are 120 pages to be typed. According to the question, the first 60 pages would be typed in 6 days. And the remaining 60 pages will be typed in 2 days at the rate of 30 pages a day. So, total number of days to type 120 pages is 8, which does not average to 20 pages a day.

Let the number of pages of the manuscript be $x$ . Let the number of days required to complete the manuscript be $y_t$ .

Now, we know that $\dfrac{x}{y_t} = 20$

The daughter completes half the manuscript, $\dfrac{x} {2}$ , at an average rate of $10$ pages in $y_1$ days. Thus, $\dfrac{\dfrac{x}{2}}{y_1} = 10$ and $y_1 = \dfrac{x}{20}$ . Let this be equation 1.

The other half, $\dfrac{x}{2}$ , at an average rate of $20$ pages in $y_2$ days. $\dfrac{\dfrac{x}{2}}{y_2} = 30$ and $y_2 = \dfrac{x}{60}$ . Let this be equation 2.

Add equation 1 and 2,

$y_1 + y_2 = \dfrac{x}{20} + \dfrac{x}{60} = \dfrac{4x}{60} = \dfrac{x}{15}$

Thus, $\dfrac{x}{(y_1 + y_2)} = 15$ . The average speed here was $15$ pages per day. The promised pages were $20$ and thus the mother was right.

let time to write first half of the manuscript = x at rate of writing = 10 pages/day then number of pages of first half = 10x pages

let time to write second half of the manuscript = y at rate of writing = 30 pages/day then number of pages of second half = 30y pages since: number of pages of first half = number of pages of second half then : 10x=30y so ---> [ x= 3y ] ----*

total number of pages of the manuscript = 2 times of number of pages of second half = 2*30y= 60y total time of writing the whole manuscript = x+y =3y+y= 4y average rate of writing = total number of pages of whole manuscript / total time taken to write it = 60y/4y

average rate of writing= 15 pages/day so : mother is right

Given that the Daughter can type an average of 20 pages a day

i.e.,In x days she can type (20*x) pages

But the first (10 x) pages will be typed @ 10 pages a day.So it takes x days to type (10 x) pages @10 pages a day

This is equal to the no: of days needed to type (20*x) pages.

So the total time would be more than the actual time

Let us assume that the total no. of pages are $100$ .

If the daughter types average 20 pages per day , she should take $\frac{100}{20}=5$ days.

But, the daughter types 1st half(i.e., 50 pages) at 10 pages a day, so she took $\frac{50}{10}=5$ days to type 1st half and the 2nd half(i.e, 50 pages), she types them at the rate of 30 pages a day, so she took $\frac{50}{30}=1.67$ days to type the 2nd half. So, she takes $5+1.67=6.67$ days which is greater than 5 days.

Thus, she did average less than 20 pages a day and so her Mother was right.

If the manuscript was 100 pages long, then it would have taken her 5 days to complete it by doing 20 pages per day. However, if she did half of it--that is, 50 pages--at a rate of 10 pages per day, then she already hit the 5 day limit and only finished half of the manuscript! Therefore, the mother was correct.

simple logic

The time in which she would have written the whole manuscript is been consumed to write only half of it.

Try the formula total Distance(D)/Total Time(T)

Avg. Speed = x/(x/20+x/30) which equals 12km/hr