Question

Jayden has been reading a 275-page book for English class. On average, he has read about 10 pages in 15 minutes. With a deadline looming, Jayden realizes that he won't finish in time unless he skims through the rest of the book. If he skims the book, he can cover 15 pages in 10min. If it takes Jayden 55 hours and 50min to finish the book (reading and skimming combined), how many pages did Jayden have to skim through?

Answer 1

75 pages

Explanation:

As with any rate, ...

... time = (task quantity)/(rate of task completion)

We assume the total time is 5 hours 50 minutes, or 350 minutes. (not 55+ hours)

... 350 min = (x pages reading)/(10/15 pages/min reading) +(y pages skimming)/(15/10 pages/min skimming) . . . . . equation 1

... x pages reading + y pages skimming = 275 pages . . . . . equation 2

Using equation 2, we can write an expression for x:

... x = 275 - y

Then we can substitute that into equation 1:

... 350 = (3/2)(275 -y) + (2/3)y

... 350 = 412.5 - (5/6)y

... -62.5 = -(5/6)y

... (62.5)(6/5) = y = 75

Jayden had to skim through 75 pages.