Tom reads at an average rate of 30 pages per hour, whil

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varun289: Master | Next Rank: 500 Posts; Posts: 298; Joined: Sun Jun 03, 2012 6:42 am; Location: New delhi; Thanked: 10 times; Followed by:7 members; GMAT Score:590

Tom reads at an average rate of 30 pages per hour, whil

by varun289 » Sun Dec 16, 2012 3:50 am

307. Tom reads at an average rate of 30 pages per hour, while Jan reads at an average rate of 40 pages per hour. If Tom starts reading a novel at 4:30, and Jan begins reading an identical copy of the same book at 5:20, at what time will they be reading the same page?
A. 9:30
B. 9:00
C. 8:40
D. 7:50
E. 7:00

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Sun Dec 16, 2012 4:16 am

varun289 wrote:307. Tom reads at an average rate of 30 pages per hour, while Jan reads at an average rate of 40 pages per hour. If Tom starts reading a novel at 4:30, and Jan begins reading an identical copy of the same book at 5:20, at what time will they be reading the same page?

In 1 minute,

Tom reads 1/2 page
Jan reads 2/3 page

4:30 to 5:20 = 50 minutes

In 50 minutes Tom has already read 50/2 = 25 pages

Say, after t minutes from 5:20, they'll be reading the same page.
Then in t minutes, Jan has to read 25 pages and the pages Tom have read in t minutes.

Hence, (25 + t/2) = 2t/3 ---> (2t/3 - t/2) = 25 ---> t/6 = 25 ---> t = 150

150 minutes after 5:20 = 2 hours 30 minutes after 5:20 = 7:50

The correct answer is D.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Sun Dec 16, 2012 4:19 am

varun289 wrote:307. Tom reads at an average rate of 30 pages per hour, while Jan reads at an average rate of 40 pages per hour. If Tom starts reading a novel at 4:30, and Jan begins reading an identical copy of the same book at 5:20, at what time will they be reading the same page?
A. 9:30
B. 9:00
C. 8:40
D. 7:50
E. 7:00

From 4:30 to 5:20, the number of pages read by Tom = r*t = 30(5/6) = 25.

From 5:20pm on, Jan COMPETES with Tom.
When elements compete, SUBTRACT THE RATES.
Jan's rate - Tom's rate = 40-30 = 10.
This is the CATCH-UP rate: the rate at which Jan CATCHES UP to Tom.
Because Jan reads 10 more pages than Tom every hour, she CATCHES-UP by 10 pages every hour.

Time for Jan to catch up by 25 pages = w/r = 25/10 = 2.5 hours.
Since Jan starts to read at 5:20pm, she catches-up to Tom at 5:20pm + 2:30 = 7:50pm.

The correct answer is D.

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nisagl750: Master | Next Rank: 500 Posts; Posts: 145; Joined: Tue Jan 31, 2012 6:50 am; Location: New Delhi; Thanked: 16 times; Followed by:2 members; GMAT Score:760

by nisagl750 » Sun Dec 16, 2012 6:32 am

Anurag@Gurome wrote: Hence, (25 + t/2) = 2t/3 ---> (2t/3 - t/2) = 25 ---> t/6 = 25 ---> t = 150

How to get the above equation? can you explain?
In such cases how to form equations?

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ritind: Senior | Next Rank: 100 Posts; Posts: 47; Joined: Wed Nov 21, 2012 10:40 pm; Thanked: 4 times

by ritind » Mon Dec 17, 2012 3:40 am

Tom - 30pages/hr
Jan - 40pages/hr
Jan would have read 10 pages more by the end of the hour

Tom starts at 4:30
by 5:20 he would have read 25 pages and Jan will start reading nw

If it takes ,
1hr - 10pages (Jan needs 1hr to cover a difference of 10pages)
xhrs - 25pages

x=2hr 30mins

5:20 + 2hrs30 mins = 7:50pm

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Mon Dec 17, 2012 3:46 am

nisagl750 wrote:
Anurag@Gurome wrote: Hence, (25 + t/2) = 2t/3 ---> (2t/3 - t/2) = 25 ---> t/6 = 25 ---> t = 150
How to get the above equation? can you explain?

Say, after t minutes from 5:20, they'll be reading the same page.
Then in t minutes, Jan has to read 25 pages and the pages Tom have read in t minutes.

Now, in t minutes,

Tom will read t/2 pages
Jan will read 2t/3 pages

Hence, in t minutes Jan will read 2t/3 pages which must be equal to (25 pages + whatever Tom has read in t minutes, i.e. t/2 pages).
Hence, (25 + t/2) = 2t/3 ---> (2t/3 - t/2) = 25 ---> t/6 = 25 ---> t = 150

Hope that helps.

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sharoonsaleem: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Sat Sep 29, 2012 3:22 am; Location: Pakistan; Thanked: 1 times; Followed by:1 members

by sharoonsaleem » Fri Dec 21, 2012 6:41 am

Ok so Tom has a head start of:
use S=Vt; P=30(50/60) = 25 pages

So assuming time clock starts to tick at 5:20

Tom's equation : S+25 = 30t

Other Guy's Equation: S=40t

Since they have to be at the same page both S are same

30t-25=40t

Which gives out t=2.5 hours : hence 7:50 Answer

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