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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Karishma
Veritas Prep GMAT Instructor
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