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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 ## Frank and Georgia started traveling from A to B at... tagged by: BTGmoderatorLU ##### This topic has 3 expert replies and 1 member reply ### Top Member ## Frank and Georgia started traveling from A to B at... Frank and georgia started traveling from A to B at the same time. Georgia's constant speed was 1.5 times Frank's constant speed. Whne Georgia arrived at B, she turned right around and returned by the same route. She cross paths with Frank, who still was coming toward B, when they were 60 miles away from B. How far away are A and B? A. 72 miles B. 120 miles C. 144 miles D. 240 miles E. 300 miles The OA is E. I'm really confused with this PS question. Experts, any suggestion about how to solve it? Thanks in advance. ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15387 messages Followed by: 1872 members Upvotes: 13060 GMAT Score: 790 Top Reply LUANDATO wrote: Frank and georgia started traveling from A to B at the same time. Georgia's constant speed was 1.5 times Frank's constant speed. When Georgia arrived at B, she turned right around and returned by the same route. She cross paths with Frank, who still was coming toward B, when they were 60 miles away from B. How far away are A and B? A. 72 miles B. 120 miles C. 144 miles D. 240 miles E. 300 miles Let d = the distance between A and B. Georgia travels the total distance in red: A------------------------------------------->B A................................................<-----60-----B Since Georgia travels the distance between A and B plus an additional 60 miles, Georgia's distance = d+60. Frank travels the distance in blue: A----------------------------->.........60.........B Since Frank travels the distance between A and B except for the last 60 miles, Frank's distance = d-60. Since Georgia's rate is 3/2 Frank's rate -- and the two travel for the same amount of time -- Georgia's distance must be 3/2 Frank's distance: d+60 = (3/2)(d-60) 2d + 120 = 3(d-60) 2d + 120 = 3d - 180 300 = d. The correct answer is E. _________________ 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. ### Top Member Master | Next Rank: 500 Posts Joined 15 Oct 2009 Posted: 331 messages Upvotes: 27 LUANDATO wrote: Frank and georgia started traveling from A to B at the same time. Georgia's constant speed was 1.5 times Frank's constant speed. Whne Georgia arrived at B, she turned right around and returned by the same route. She cross paths with Frank, who still was coming toward B, when they were 60 miles away from B. How far away are A and B? A. 72 miles B. 120 miles C. 144 miles D. 240 miles E. 300 miles The OA is E. I'm really confused with this PS question. Experts, any suggestion about how to solve it? Thanks in advance. Helps to visualize or draw a diagram. Calling the distance between A and B, "D", recognize that she has traveled that full distance and then an additional 60 miles back toward A when she meets Frank So the distance Georgia travels is D+60. Call Frank's speed R, so her speed is 1.5*R. Use D=R*T, D+60 = 1.5R x T Over this same time recognize that Frank has traveled to a point 60 miles short of B, so his distance traveled is D - 60 = R x T Use this equation to eliminate D = R x T + 60. Substitute this into the first equation: R x T + 60 + 60 =1.5R x T Simplify, 0.5R x T = 120 > R x T = 240 See from above that D is R x T +60, so D = 240 + 60 = 300 , E ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2666 messages Followed by: 125 members Upvotes: 1153 GMAT Score: 770 LUANDATO wrote: Frank and georgia started traveling from A to B at the same time. Georgia's constant speed was 1.5 times Frank's constant speed. Whne Georgia arrived at B, she turned right around and returned by the same route. She cross paths with Frank, who still was coming toward B, when they were 60 miles away from B. How far away are A and B? A. 72 miles B. 120 miles C. 144 miles D. 240 miles E. 300 miles The OA is E. I'm really confused with this PS question. Experts, any suggestion about how to solve it? Thanks in advance. Let's say Georgia's speed is 30 mph and Frank's is 20 mph. (We could have picked any numbers so that Georgia's speed was 1.5 times that of Frank's.) And say they travel for t hours. Georgia's total distance = 30t Frank's total distance = 20t Now we know that Georgia will have covered 120 miles more than Frank. (Frank stops 60 miles short of B. Georgia will cover those 60 miles to B, and then 60 miles back to meet Frank.) Thus 30t = 20t + 120 10t = 120 t = 12 So Frank's total distance is 20t = 20*12 = 240. If he was 60 miles short of B, then the total distance from A to B is 240 + 60 = 300. The answer is E _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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LUANDATO wrote:
Frank and georgia started traveling from A to B at the same time. Georgia's constant speed was 1.5 times Frank's constant speed. Whne Georgia arrived at B, she turned right around and returned by the same route. She cross paths with Frank, who still was coming toward B, when they were 60 miles away from B. How far away are A and B?

A. 72 miles
B. 120 miles
C. 144 miles
D. 240 miles
E. 300 miles
We can let r = Frankâ€™s speed and 1.5r = Georgiaâ€™s speed. Also, we can let the distance between A and B = d.

Since they met at 60 miles away from B, we see that the time Frank spent on driving 60 miles less than the distance between A and B is the same as the time Georgia spent on driving 60 miles more than the distance between A and B. Thus we can create the following equation:

(d - 60)/r = (d + 60)/1.5r

1.5r(d - 60) = r(d + 60)

1.5(d - 60) = d + 60

1.5d - 90 = d + 60

0.5d = 150

d = 300

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