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

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Manager
Joined: 11 Feb 2011
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Tom reads at an average rate of 30 pages per hr while jan re [#permalink]

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15 Jun 2011, 10:58
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71% (02:06) correct 29% (01:19) wrong based on 21 sessions

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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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Senior Manager
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15 Jun 2011, 13:08
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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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15 Jun 2011, 20:22
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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

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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Intern
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16 Jun 2011, 11:40
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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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Director
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05 Aug 2011, 12:05
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

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Manager
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05 Aug 2011, 12:20
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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Kaustubh

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28 Sep 2013, 07:38
Hello from the GMAT Club BumpBot!

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Re: Tom reads at an average rate of 30 pages per hr while jan re [#permalink]

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03 Feb 2014, 10:35
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

Rgds
Prasannajeet

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Re: Tom reads at an average rate of 30 pages per hr while jan re [#permalink]

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29 Mar 2014, 00:40
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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]

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18 May 2015, 00:57
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Senior Manager
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Re: Tom reads at an average rate of 30 pages per hr while jan re [#permalink]

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22 Jun 2015, 03:55
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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.

Kudos [?]: 134 [1], given: 169

Re: Tom reads at an average rate of 30 pages per hr while jan re   [#permalink] 22 Jun 2015, 03:55
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