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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 ## Sanjana jogged uphill for a while at an average speed of 3 m tagged by: Anaira Mitch ##### This topic has 4 expert replies and 3 member replies ## Sanjana jogged uphill for a while at an average speed of 3 m ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Sanjana jogged uphill for a while at an average speed of 3 miles per hour, then jogged downhill for a while at an average speed of 8 miles per hour. If Sanjana jogged the uphill and downhill stretches in a total of 40 minutes at an average speed of 4 miles per hour, how far did she jog uphill? A. 1 mile B. 1 1/3 miles C. 1 1/2 miles D. 1 3/5 miles E. 1 2/3 miles ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 13001 messages Followed by: 1250 members Upvotes: 5254 GMAT Score: 770 Top Reply Anaira Mitch wrote: Sanjana jogged uphill for a while at an average speed of 3 miles per hour, then jogged downhill for a while at an average speed of 8 miles per hour. If Sanjana jogged the uphill and downhill stretches in a total of 40 minutes at an average speed of 4 miles per hour, how far did she jog uphill? A. 1 mile B. 1 1/3 miles C. 1 1/2 miles D. 1 3/5 miles E. 1 2/3 miles Let's start with a "Word Equation" (distance traveled uphill) + (distance traveled downhill) = TOTAL DISTANCE Let t = the time spent jogging UPHILL (in hours) The total travel time = 40 minutes = 2/3 HOURS So, 2/3 - t = the time spent jogging DOWNHILL (in hours) Distance = (speed)(time) So, we can rewrite our word equation as: 3t + 8(2/3 - t) = (4)(2/3) Expand to get: 3t + 16/3 - 8t = 8/3 Subtract 16/3 from both sides to get: 3t - 8t = -8/3 Simplify to get: -5t = -8/3 Solve: t = (-8/3)/(-5) = 8/15 So, Sanjana spent 8/15 hours traveling UPHILL How far did Sanjana jog uphill? Distance = (speed)(time) So distance = (3)(8/15) = 8/5 = 1 3/5 miles Answer: D Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use my video course along with Sign up for free Question of the Day emails And check out all of these free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! Newbie | Next Rank: 10 Posts Joined 19 Nov 2018 Posted: 7 messages Answer is D The total distance travelled in 40 minutes at average speed of 4 miles per hour is : 4*(40/60) = 8/3 miles. Now, let she jogged for x hours uphill, so time consumed jogging downhill will be (40/60)-x hours= (2/3)-x22/3 / Since total distance = distance uphill+ distance downhill => 8/3= 3*x + 8* [(2/3)-x] x=8/15 Now, distance jogged uphill= 3*x=3*8/15=13/5= 1 3/5 Hence D Master | Next Rank: 500 Posts Joined 26 Oct 2016 Posted: 235 messages Followed by: 5 members Upvotes: 3 Can this question be solved using any other approach apart from algebra? ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 13001 messages Followed by: 1250 members Upvotes: 5254 GMAT Score: 770 Anaira Mitch wrote: Can this question be solved using any other approach apart from algebra? You could also try testing the answer choices. Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use my video course along with Sign up for free Question of the Day emails And check out all of these free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! Master | Next Rank: 500 Posts Joined 26 Oct 2016 Posted: 235 messages Followed by: 5 members Upvotes: 3 Thanks Brent. ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15362 messages Followed by: 1866 members Upvotes: 13060 GMAT Score: 790 Quote: Quote: Sanjana jogged uphill for a while at an average speed of 3 miles per hour, then jogged downhill for a while at an average speed of 8 miles per hour. If Sanjana jogged the uphill and downhill stretches in a total of 40 minutes at an average speed of 4 miles per hour, how far did she jog uphill? A. 1 mile B. 1 1/3 miles C. 1 1/2 miles D. 1 3/5 miles E. 1 2/3 miles Can this question be solved using any other approach apart from algebra? This is a MIXTURE problem. Two speeds (3 mph and 8 mph) are combined to form a mixture with an average speed of 4 mph. To determine how much time must be spent at each speed, we can use ALLIGATION. Let U = the uphill speed and D = the downhill speed. Step 1: Plot the 3 speeds on a number line, with the speeds for U and D on the ends and the speed for the mixture in the middle. U 3---------4----------8 D Step 2: Calculate the distances between the values on the number line. U 3----1----4----4----8 D Step 3: Determine the time ratio for the two speeds. The time ratio for U and D is equal to the RECIPROCAL of the distances in red. U : D = 4:1. Implication: Of every 5 minutes of travel time, 4 minutes are spent at the uphill speed, while 1 minute is spent at the downhill speed. Thus, 4/5 of the total travel time is spent at the uphill speed: (4/5)(40 minutes) = 32 minutes = 32/60 hour = 8/15 hour. Since 8/15 hour is spent at the uphill speed of 3 mph, we get: Distance uphill = rt = (3)(8/15) = 8/5 = 1 3/5 miles. 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: 2852 messages Followed by: 18 members Upvotes: 43 Anaira Mitch wrote: Sanjana jogged uphill for a while at an average speed of 3 miles per hour, then jogged downhill for a while at an average speed of 8 miles per hour. If Sanjana jogged the uphill and downhill stretches in a total of 40 minutes at an average speed of 4 miles per hour, how far did she jog uphill? A. 1 mile B. 1 1/3 miles C. 1 1/2 miles D. 1 3/5 miles E. 1 2/3 miles We can let t = the number of hours Sanjana jogged uphill. Since 40 minutes = 2/3 of an hour, the time she jogged downhill was (2/3 - t) hours. We can create the equation: 3t + 8(2/3 - t) = 4(2/3) 3t + 16/3 - 8t = 8/3 -5t = -8/3 t = 8/15 Since she jogged 8/15 of an hour uphill at an average speed of 3 mph, she jogged 8/15 x 3 = 8/5 = 1 3/5 miles. 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 • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live 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 • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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