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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, 22:38
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Difficulty:

  45% (medium)

Question Stats:

68% (02:37) correct 32% (02:38) wrong based on 202 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 18 Nov 2015, 23:32
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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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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, 11:18
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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 09 Sep 2016, 10:51
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Yes, agree with all the solutions. Here is another algebraic one.

Since TOM is 25 pages ahead when Jan starts, let us take that after x hours they are at the same page. So, simple equation would be

25+30X=40X; X=2.5 hours. Adding 2.5 hours to 5:20 gives 7:50.

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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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Re: Tom reads at an average rate of 30 pages per hour, while Jan reads at   [#permalink] 11 Oct 2018, 19:19
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