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Tom reads at an average rate of 30 pages per hr while jan re

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Tom reads at an average rate of 30 pages per hr while jan re [#permalink] New post 15 Jun 2011, 09:58
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Tom reads at an average rate of 30 pages per hr while jan reads at av rate of 40 pages per hr.If tom starts reading a novel at 4:30 and jan begins 5:20 ,at what time will they be reading the same page?

OA :
[Reveal] Spoiler:
7:50

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Re: Tricky! [#permalink] New post 15 Jun 2011, 12:08
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Tom starts at 4:30, so by the time Jan begins Tom has read for 50 mins i.e. 25 pages.

we know that in 60 mins Tom reads 30 pages and Jan reads 40 pages
let x be the time when both are on the same page.
30X+25 = 40x
25 = 10x
x=25/10 = 2.5 hrs

so if Jan begin at 5:20, time when both will be together = 5:20 + 2.5 hrs = 7.50.
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Re: Tricky! [#permalink] New post 15 Jun 2011, 19:22
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AnkitK wrote:
Tom reads at an average rate of 30 pages per hr while jan reads at av rate of 40 pages per hr.If tom starts reading a novel at 4:30 and jan begins 5:20 ,at what time will they be reading the same page?
OA : 7:50

Please highlight the concept .


This is how I would solve this question:
It is a work-rate problem.
Rate of Tom = 30 pages/hr
Rate of Jan = 40 pages/hr

Question: at what time will they be reading the same page?
This translates to "at what time would they have done the same work?"
Say, they are both on page 100 of the book at some time. This means that they have done the same work as of this moment since they have both read 100 pages. Of course, since their rates of work are different, their time taken would also be different.
Rate of Tom : Rate of Jan = 3:4
Therefore, Time taken by Tom : Time taken by Jan = 4:3
This difference of 1 in their 'time taken' is equal to 50 minutes (4:30 to 5:20). Hence, Tom took 4*50 = 200 minutes from the time he started and Jan took 3*50 = 150 minutes from the time she started.
Hence, they were at the same page 2.5 hrs after Jan started i.e. at 7:50

If working with ratios did not make sense to you, check out these posts:
http://www.veritasprep.com/blog/2011/03 ... of-ratios/
http://www.veritasprep.com/blog/2011/03 ... -problems/
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Re: Tricky! [#permalink] New post 16 Jun 2011, 10:40
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consider time taken by Tom to read = t
as Jan started 50 minutes after Tom , time taken by Jan= t-50
since work done by Jan = work done by Tom
so (t-50) (2/3)= (t)(1/2)
t=200 minutes.
Adding it to 4:30 would give 7:50
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Re: Tricky! [#permalink] New post 05 Aug 2011, 11:05
T

30 pages/hour t+(50/60) hours

J

40 pages/hour t hours


at some point in time their output would be same = > work would same


=> 30(t+(5/6)) = 40t

=> t = 2.5 hours

i.e 2.5 hours from 5.30. i.e 7.50

Hence the answer is 7.50
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Re: Tricky! [#permalink] New post 05 Aug 2011, 11:20
Before jan starts tom has already read 25 pages.
therefore 30x+25=40x
solving we get x=2.5=2 hrs 30 mins
so 5 hrs 20 mins + 2 hrs 30 mins=7 hrs 50 mins
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Re: Tricky! [#permalink] New post 28 Sep 2013, 06:38
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Re: Tom reads at an average rate of 30 pages per hr while jan re [#permalink] New post 03 Feb 2014, 09:35
Tom Rate=30 page/60 min=1/2 similarly Jan Rate=40 page/60min=2/3

Lets say after Time=T both are in the same page
Now @ time T Tom will read 1/2*T=T/2 and Jan will be read 2/3*T=2T/3

But Tom starts 50 min before Jan starts reading so in 50 min Tom read =25 pages
T/2+25=2T/3 because we have considered after T Min both are in same page.
Solve T=150 min i.e 2 hour 30 min or 7.50 ans

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Re: Tom reads at an average rate of 30 pages per hr while jan re [#permalink] New post 28 Mar 2014, 23:40
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Took time in this one, though solved it lately.

Concept: Distance between tom and Jan and relative speed.

Knowing the concepts of time speed distance, we are aware that.

Time taken for Jan to catch Tom = Distance between them/ Relative speed.

Calculate distance between them:

How many pages Tom is ahead while reading for 50 minutes more than Jan

30 * 5/6 hours = 25 Pages

So Time taken for Jan to catch Tom = 25/(40-30)= 2 hours 30 minutes.

05:20 + 02:30 = 07:50
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Re: Tom reads at an average rate of 30 pages per hr while jan re [#permalink] New post 17 May 2015, 23:57
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Re: Tom reads at an average rate of 30 pages per hr while jan re [#permalink] New post 22 Jun 2015, 02:55
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I found a few very good ways to solve it above and gave my kudos.

Another one would be this one:

Tom reads 30 pages in 1 hour (60 minutes) or 0.5 pages in 1 minute.
Jan reads 40 pages in 1 hours (60 minutes) or about 0.66 pages in 1 minutes.

Tom has already been reading for 50 minutes, so he has already read 25 pages at 5:20, when Jan starts. I created the following table using this information:


...........5:20........6:20........7:20........8:20
T...........25...........55...........85.........115
J............0............40...........80.........120

So, at 8:20 Jan has aready passed Tom and at 7:20 he has almost cought up with him. It must be sometime in between. So, we break it up in minutes:

........7:20........7:30........7:40..........7:50
T.......85............90...........95..........100
J.......80...........86.6........93.2.........99.8

So, at 7:50 they will be on the same page.
Re: Tom reads at an average rate of 30 pages per hr while jan re   [#permalink] 22 Jun 2015, 02:55
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