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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## James started from his home and drove eastwards at a tagged by: BTGmoderatorLU ##### This topic has 2 expert replies and 0 member replies ### Top Member ## James started from his home and drove eastwards at a ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Source: e-GMAT James started from his home and drove eastwards at a constant speed. Exactly 90 minutes after James stated from his home, his brother Patrick started from the same point and drove in the same direction as James did at a different constant speed. Patrick overtook James exactly 90 minutes after Patrick started his journey and then continued driving at the same speed for another 2 hours. By what percentage should Patrick reduce his speed so that James could catch up with Patrick in exactly 8 hours after Patrick overtook James? A. 25% B. 33% C. 50% D. 67% E. 75% The OA is D. ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15260 messages Followed by: 1862 members Upvotes: 13060 GMAT Score: 790 BTGmoderatorLU wrote: Source: e-GMAT James started from his home and drove eastwards at a constant speed. Exactly 90 minutes after James stated from his home, his brother Patrick started from the same point and drove in the same direction as James did at a different constant speed. Patrick overtook James exactly 90 minutes after Patrick started his journey and then continued driving at the same speed for another 2 hours. By what percentage should Patrick reduce his speed so that James could catch up with Patrick in exactly 8 hours after Patrick overtook James? A. 25% B. 33% C. 50% D. 67% E. 75% Let James' rate = 3 mph. James started from his home and drove eastwards at a constant speed. Exactly 90 minutes after James stated from his home, his brother Patrick started from the same point and drove in the same direction as James did at a different constant speed. Patrick overtook James exactly 90 minutes after Patrick started his journey. When James is overtaken by Patrick, James has traveled for a total of 3 hours, implying the following distance: rt = 3*3 = 9 miles. Patrick leaves 90 minutes after James and thus overtakes James by traveling these 9 miles in only 1.5 hours, implying the following rate for Patrick: d/t = 9/(1.5) = 90/15 = 6 mph. Patrick then continued driving at the same speed for another 2 hours. When people COMPETE, we SUBTRACT THEIR RATES. Difference between Patrick's rate and James' rate = 6-3 = 3 mph. Implication: Every hour after overtaking James, Patrick travels 3 miles ahead of James. Thus: Over the next 2 hours, Patrick travels a total of 6 miles head of James. By what percentage should Patrick reduce his speed so that James could catch up with Patrick in exactly 8 hours after Patrick overtook James? Since 2 hours have passed since Patrick overtook James, James must catch up to Patrick in the next 6 hours. Implication: For James to catch up by 6 miles over the next 6 hours, he must catch up by 1 mile every hour. Thus: Over the next 6 hours, James' rate must be ONE MPH GREATER than Patrick's rate, so that James catches up by 1 mile every hour. Since James' rate = 3 mph, Patrick's rate must decrease from 6 mph to 2 mph. Percent decrease from 6 to 2 = Difference/Larger * 100 = (6-2)/6 * 100 = 66.66%. The correct answer is D. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2456 messages Followed by: 18 members Upvotes: 43 BTGmoderatorLU wrote: Source: e-GMAT James started from his home and drove eastwards at a constant speed. Exactly 90 minutes after James stated from his home, his brother Patrick started from the same point and drove in the same direction as James did at a different constant speed. Patrick overtook James exactly 90 minutes after Patrick started his journey and then continued driving at the same speed for another 2 hours. By what percentage should Patrick reduce his speed so that James could catch up with Patrick in exactly 8 hours after Patrick overtook James? A. 25% B. 33% C. 50% D. 67% E. 75% The OA is D. We can let Jamesâ€™ speed be 60 mph. Thus, when James drove 180 minutes (or 3 hours), Patrick drove only 90 minutes. So James drove 60 x 3 = 180 miles. Although Patrick only drove 90 minutes (or 1.5 hours), he drove the same distance as James (since he overtook James exactly in 90 minutes), so Patrick drove at a speed of 180/1.5 = 120 mph. He continued at this speed for another 2 hours, which means he drove another 2 x 120 = 240 miles. He will drive another 6 hours, however, at a slower speed, so that James could catch up with him exactly 8 hours after overtaking James. We can let this new speed be x. So the total distance Patrick travels is 180 + 240 + 6x = 420 + 6x. Now letâ€™s look at the distance James traveled. Recall that he had to catch up with Patrick exactly 8 hours after Patrick overtook him. When Patrick overtook him, each had driven 180 miles. Since Jamesâ€™ speed was 60 mph (and he continued to drive at that speed), then, in another 8 hours, he will have driven 60 x 8 = 480 miles. Thus the total distance James will have traveled is 180 + 480 = 660. Now we can equate the distances traveled by the two brothers as follows: 420 + 6x = 660 6x = 240 x = 40 Since Patrickâ€™s original speed was 120 mph and his new speed is 40 mph, he must have reduced his original speed by 2/3, or 67%. Answer: D _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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