Who is right?

Algebra Level 2

Kate is writing her first novel.

At first, things went slowly. For the first half (in terms of number of pages) of the novel, she was only able to produce 5 pages per day on the manuscript.

Then she had a burst of creative inspiration. For the second half of the manuscript, she churned out work at the rate of 15 pages per day, before finishing the draft and sending it to the publishing house.

She told her mom this, and concluded proudly, "I averaged 10 pages per day."

"No, you didn't," her mom replied.

Who is right?

Kate Her mom Not enough information to determine

2 solutions

Denton Young
Aug 4, 2017

Let's say the novel is $x$ pages long. It took Kate $x/5$ days to write the first half of it and $x/15$ days to write the second half.

So the total time taken is $4x/30$ days. So she averaged $x\div (4x/30)$ pages per day, which is $7.5$ pages per day.

Was this taken from the Moscow Puzzles? I have the book and I recognized this problem!

Amogha Pokkulandra - 3 years, 10 months ago

No, but that book (I read it when I was in high school) has so many problems -- close to 400 -- that it's inevitable that some problems people submit will be similar.

Denton Young - 3 years, 10 months ago

If the novel is x pages long, it think it would take her x/2/5 for the first half and x/2/15 for the second half. For instance, if the novel is 60 pages, it took (60/2/5) 6 days to write the first half and only (60/2/15) 2 days to write the second. However, I think you made a correcting mistake while solving the equation because when you added x/5 and x/15 you got 4x/30 when really that should have been 4x/15.

Joe Aulicino - 3 years, 10 months ago

Azadali Jivani
Aug 4, 2017

Suppose total pages = 150
75 pages written in 15 days....[given; 5 pages written/day ]
and..other 75 pages written in 5 days [given; 15 pages written/day ]
so..150 pages in 20 days
therefore average = 150/20 = 7.5