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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 ## David covers a total of 240 miles journey, of which tagged by: Vincen ##### This topic has 2 expert replies and 0 member replies ### Top Member ## David covers a total of 240 miles journey, of which David covers a total of 240 miles journey, of which 120 miles are covered at a constant speed and remaining 120 miles are covered at 10 mph more than first half speed. The Time took to cover the second half of 240 miles is 1 hour less than the first half of 240 miles. At what speed did David cover his second half of the journey? (A) 30 mph (B) 35 mph (C) 40 mph (D) 45 mph (E) 50 mph The OA is the option C. Experts, may you help me here? I don't know what are the equations I should set here. ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Top Reply Quote: David covers a total of 240 miles journey, of which 120 miles are covered at a constant speed and remaining 120 miles are covered at 10 mph more than first half speed. The Time took to cover the second half of 240 miles is 1 hour less than the first half of 240 miles. At what speed did David cover his second half of the journey? (A) 30 mph (B) 35 mph (C) 40 mph (D) 45 mph (E) 50 mph The OA is the option C. Experts, may you help me here? I don't know what are the equations I should set here. Hi Vincen, Let's take a look at your question. Let the first half of 120 miles journey is covered at a constant speed of x miles/hr. Then the second half of 120 miles journey will be covered in (x+10) miles/hr. Let the time taken to cover the first half of journey is y hours. Then the time taken to cover the second half of journey will be (y-1) hours. We know that: $$Distance\ =\ Speed\ \times\ Time$$ Using Distance formula, we can write two equations for first half and second half of the journey. $$120=xy...\left(i\right)$$ $$120=\left(x+10\right)\left(y-1\right)...\left(ii\right)$$ LHS of both equations is the same i.e. 120, so we will equate the RHS of the equations. $$xy=\left(x+10\right)\left(y-1\right)$$ $$xy=xy-x+10y-10$$ $$0=-x+10y-10$$ $$x=10y-10 ... (iii)$$ Substitute the value of x from equation (iii) in eq(i), we get: $$\left(10y-10\right)y=120$$ $$10\left(y-1\right)y=120$$ $$\left(y-1\right)y=12$$ $$y^2-y=12$$ $$y^2-y-12=0$$ Factorize to find y: $$y^2-4y+3y-12=0$$ $$y\left(y-4\right)+3\left(y-4\right)=0$$ $$\left(y+3\right)\left(y-4\right)=0$$ $$y=-3,\ 4$$ Since, y represents time and time can not be negative, therefore, we will discard y = -3 and consider only: $$y=4$$ Plugin y = 4 in eq(i) to find y to find y: $$xy=120$$ $$x\left(4\right)=120$$ $$x=\frac{120}{4}=30$$ We are asked to find the speed of the second half of the journey i.e. represented by x+10. $$Speed\ of\ second\ half=x+10=30+10=40mph$$ Therefore, Option C is correct. Hope this helps. I am available if you'd like any follow up. _________________ GMAT Prep From The Economist We offer 70+ point score improvement money back guarantee. Our average student improves 98 points. Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now. ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15387 messages Followed by: 1872 members Upvotes: 13060 GMAT Score: 790 Vincen wrote: David covers a total of 240 miles journey, of which 120 miles are covered at a constant speed and remaining 120 miles are covered at 10 mph more than first half speed. The Time took to cover the second half of 240 miles is 1 hour less than the first half of 240 miles. At what speed did David cover his second half of the journey? (A) 30 mph (B) 35 mph (C) 40 mph (D) 45 mph (E) 50 mph We can PLUG IN THE ANSWERS, which represent the greater of the two speeds. When the correct answer is plugged in, the time difference for the two speeds will be 1 hour. Since the time difference is an INTEGER VALUE, it is almost guaranteed that the two speeds will divide evenly into the 120-mile distance. Since the lower speed is 10mph less than the greater speed, the answer choices imply the following options for the two speeds: A: 30mph, 20mph --> each is a factor of 120 B: 35mph, 25mph --> neither is a factor of 120 C: 40mph, 30mph --> each is a factor of 120 D: 45mph, 35mph --> neither is a factor f120 E: 50mph, 40mph --> 50 is not a factor of 120 The correct answer is almost certainly A or C. C: 30mph, 40mph At 30mph, the time to travel 120 miles = d/r = 120/30 = 4 hours. At 40mph, the time to travel 120 miles = d/r = 120/40 = 3 hours. Time difference = 4-3 = 1 hour. Success! The correct answer is C. _________________ 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. • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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