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Tricky!

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Tricky! [#permalink]  15 Jun 2011, 10:58
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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 : 7:50

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Re: Tricky! [#permalink]  15 Jun 2011, 13:08
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]  15 Jun 2011, 20:22
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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Re: Tricky! [#permalink]  16 Jun 2011, 11:40
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]  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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Re: Tricky! [#permalink]  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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Re: Tricky!   [#permalink] 05 Aug 2011, 12:20
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