Mork reads at an average rate of 30 pages per hour, while Mindy reads at an average rate of 40 pages per hour. If Mork starts reading a novel at 4:30, and Mindy begins reading an identical copy of the same book at 5:20, at what time will they be reading the same page?
We're told to figure out when Mindy will catch up with Mork. Mindy reads at the rate of 40 pages per hour and Mork reads at the rate of 30 pages per hour. Mork starts reading 50 minutes ahead of Mindy. Since 50 minutes is 5/6 of an hour, by the time Mindy starts reading at 5:20, Mork has already read 5/6 x 30 = 25 pages. You might have saved yourself some work by noticing that Mindy gains 10 pages an hour on Mork, since she reads 10 pages an hour faster. Since he's got a head start of 25 pages at 5:20, it should take her 25 (pages) divided by 10 (pages per hour), or 2.5 (hours) to catch him. Since Mindy started at 5:20, this means she'll catch up to Mork at precisely 7:50.

You can also work out the problem algebraically. The number of pages Mindy has read at any given time after 5:20 is 40t, where t is the time in hours from 5:20. At 6:20 she's read 40 pages, at 7:20 she's read 80 pages, etc. The number of pages that Mork has read at any time after 5:20 is 25 + 30t. We want to know when these quantities will be equal, that is, when 25 + 30t = 40t. Solving for t we get 25 = 40t - 30t, 25 = 10t, 2.5 = t. So it takes 2.5 hours for Mindy to catch Mork.

The source of this solution is The Kaplan Edge.

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A SureMath solution. Copyright 1998, Howard C. McAllister.