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

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Tom reads at an average rate of 30 pages per hour, while Jan reads at  [#permalink]

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New post 18 Nov 2015, 23:38
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Question Stats:

71% (02:28) correct 29% (02:36) wrong based on 216 sessions

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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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Re: Tom reads at an average rate of 30 pages per hour, while Jan reads at  [#permalink]

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New post 29 Nov 2015, 12:18
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Hi All,

This is an example of a 'chase down' question (wherein one entity tries to 'chase down' another entity that has a head start on some task).

We're told that Tom reads 30 pages/hour and Jan reads 40 pages/hour. Tom starts reading a book at 4:30pm and Jan starts reading the same book at 5:20pm. We're asked at what time they'll be on the same page (in other words, when will Jan chase down Tom).

Since Tom has a 50 minute head start, we can calculate how many pages he's read before Jan gets started...

50 minutes = 5/6 hour
(5/6 hour)(30 pages/hour) = 25 pages

So Tom has a 25 page head-start when Jan starts reading. She will end up reading 10 MORE pages per hour than Tom reads, so she will chase-down 10 pages per hour.

25 pages/10 per hour = 2.5 hours FROM the point that SHE starts reading.

5:20pm + 2.5 hours = 7:50pm

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Re: Tom reads at an average rate of 30 pages per hour, while Jan reads at  [#permalink]

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New post 19 Nov 2015, 00:32
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1
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relative speed =jan - Tom =10 pages per hour = 1/6 page per minute
time diff =50 minutes
by the time Jan started ToM already finished (30/60)*50 = 25 pages
time taken = 25 /(1/6) =25*6= 150 minutes
7:50
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Tom reads at an average rate of 30 pages per hour, while Jan reads at  [#permalink]

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New post 09 Sep 2016, 11:51
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Bunuel wrote:
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



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: Tom reads at an average rate of 30 pages per hours, while  [#permalink]

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Re: Tom reads at an average rate of 30 pages per hours, while   [#permalink] 30 Sep 2019, 03:15
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