Question

If Jayden is reading a 275 page book and can read 10 pages in 15 minutes, skim through 15 pages in 10 minutes, and finishes the book in 5 hours and 50 minutes (reading and skimming combined), how many pages did Jayden have to skim through?

Answer 1

Jayden skim 75 pages.

Explanation:

Consider the provided information.

First convert hours into minutes: 5 hours and 50 minutes can be written as:

5 × 60 + 50 = 350 minutes

let x is the number of minutes spent skimming. then the time spent in reading is (350-X).

He can read 10 pages in 15 minutes, skim through 15 pages in 10 minutes, and there are 275 page in book.

`x* (15)/(10)+ (350 - x) * (10)/(15)= 275`

Now, solve for X.

`x* (3)/(2)+ (350 - x) * (2)/(3)= 275`

`(9x+4(350-x))/(6)=275`

`9x+1400-4x=1650`

`5x=250`

`x=50`

Hence, Jayden spent 50 minutes skimming.

The rate of 15 pages every 10 minutes, Thus the number of pages he skimmed is:

`50* (15)/(10)= 5* 15=75`

Hence, he skim 75 pages.

Answer 2

Jayden skimmed through 75 pages.

Explanation:

Jayden is reading 275 page book.

Let Jyden read number of pages = x

and skimmed through pages = (275 -x)

Since Jayden read 10 pages in 15 minutes.

So time taken to read x pages =
`(15* x)/(10)` minutes

and Jayden skim through 15 pages in 10 minutes

So time taken to skim (275-x) pages =
`(10)/(15)`× (275-x)

Now we know Jayden took total time to read and skim the book = 5 hours and 50 minutes.

so
`(15)/(10)x+ (10)/(15)(275-x)=350`

Multiply equation by 15.

22.5x + 10(275-x) = 350×15

22.5x + 2750 - 10x = 5250

12.5x = 5250 - 2750

12.5x = 2500

x =
`(2500)/(12.5)`

x = 200

Pages skimmed through = 275 - 200 = 75

Therefore, pages read by Jayden is 200 pages and skim through 75 pages.