Question

Jayden has been reading 275-page book for English class. On average, he has read about 10 pages in 15 minutes (min). 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 10 min. If it takes Jayden 5 hours and 50 min to finish the book (reading and skimming combined), how many pages did Jayden have to skim through?

A. 50

B. 75

C. 200

D. 350

Answer 1

Jayden's usual reading rate is (4*15 min)/(4*10 pages) = (1 h)/(40 pages). His skimming rate is (6*10 min)/(6*15 pages) = (1 h)/(90 pages). If s represents the number of pages Jayden skimmed, then his total reading time for 275 pages is
.. s pages*(1 h/(90 pages)) + (275 -s) pages*(1 h/(40 pages)) = 5 5/6 h
.. 4s +9(275 -s) = 360*(5 5/6) . . . . . . . multiply by the common denominator, 360
.. -5s = 2100 -2475 . . . . . . . . . . . . . . . collect terms, subtract 9*275
.. s = -375/-5 = 75 . . . . . . . . . . . . . . . . divide by the coefficient of s

Jayden skimmed 75 pages, selection B.