At a constant hourly rate, Mark had estimated

Question

At a constant hourly rate, Mark had estimated that he could read a book of 450 pages in a designated time, and he started reading the book. However, Mark took 3 hours longer than he had estimated, and, consequently, he finished 5 pages per hour less than his constant hourly rate. What was the time, in hours, that Mark had estimated for reading the complete book?

(a) 15
(b) 18
(c) 20
(d) 23
(e) None

(a) 15
(b) 18
(c) 20
(d) 23 
(e) None

chetan2u · Answer

Let the speed be x pages per hour, so time taken in hours =  \frac{450}{x}

At a slower speed of x-5, time taken =  \frac{450}{x-5}

\frac{450}{x}+3=\frac{450}{x-5}...................450x-450*5+3*x(x-5)=450x.............3*x*(x-5)=450*5=3*150*5=3*30*25

So initial speed was 30 pages per hour. Time taken =  \frac{450}{30}=15

A

Crytiocanalyst · Answer

let p be the number of pages read in 1 hour and t be the total time taken 
=>450/t = p.......2

Through second information we can estimate 450 / p-5 = t+3 ......1
Upon solving for t from 2 and 1 we get 
t^2 +3t -270 =0
=> t=15 and t=-18

Therefore IMO A

SaquibHGMATWhiz · Answer

Solution:

Let us assume that Mark estimated that he can read x pages per hour 
 Time he was supposed to take based on the above estimation  =\frac{450}{x}

Mark read at the rate of (x - 5) pages per hour 
 Time he took based on the above rate  =\frac{450}{x-5}

According to the question,  \frac{450}{x-5}-\frac{450}{x}=3 
 ⇒\frac{450x-450(x-5)}{x(x-5)}=3 
 ⇒450x-450x+2250=3x^2-15x 
 ⇒3x^2-15x-2250=0 
 ⇒x^2-5x-750=0 
 ⇒x^2-30x+25x-750=0 
 ⇒x(x-30)+25(x-30)=0 
 ⇒x=30  or  x=-25 (can be ignored because rate cannot be negative)

Thus time Mark had estimated for reading the complete book  =\frac{450}{x}=\frac{450}{30}=15  hours

Hence the right answer is    Option A

Gemmie · Answer

Estimated time: t
Estimated speed: s

s * t = (s - 5) (t+3) = 450

From the answer choices, start with an answer easily dividing 450

Answer choice A is already a good one

450 = 30        * 15  
      = 25   * 18

==> This answer choice fits
==> Answer choice A

At a constant hourly rate, Mark had estimated

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At a constant hourly rate, Mark had estimated

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