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Distance

This topic has 3 expert replies and 0 member replies
datonman Senior | Next Rank: 100 Posts Default Avatar
Joined
28 May 2014
Posted:
53 messages

Distance

Post Wed Nov 04, 2015 9:25 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    During a trip, Francine traveled 'x' percent of the total distance at an average speed of 40 miles per hour and the rest of the distance at an average speed of 60 miles per hour. In terms of 'x', what was Francine's average speed for the entire trip?

    A.)180-x/2
    B.)x + 60/4
    C.)300-x/5
    D.)600/115-x
    E.)12,000/x+200

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    Post Wed Nov 04, 2015 10:14 am
    NOTE: I added some brackets to avoid ambiguity.

    Quote:
    During a trip, Francine traveled x percent of the total distance at an average speed of 40 miles per hour and the rest of the distance at an average speed of 60 miles per hour. In terms of x, what was Francine's average speed for the entire trip?

    A. (180-x)/2
    B. (x+60)/4
    C. (300-x)/5
    D. 600/(115-x)
    E. 12,000/(x+200)
    Here's an algebraic approach.
    I like to begin with a word equation:
    Average speed = (total distance)/(total time)
    For this question, let's let the total distance = D

    Next, observe that: total time = (time spent driving 40 mph) + (time spent driving 60 mph)

    time spent driving 40 mph = distance/speed
    Aside: distance driven = (x/100)(D)
    So, time spent driving 40 mph = (x/100)(D)/40


    time spent driving 60 mph = distance/speed
    Aside: if x% of the distance was driven at 40 mph, then the distance driven at 60 mph = [(100-x)/100](D)
    So, time spent driving 60 mph = [(100-x)/100](D)/60


    Here comes the awful algebra ...

    Total time = (x/100)(D)/40 + [(100-x)/100](D)/60
    Simplify ...
    Total time = xD/4000 + [100D-xD]/6000
    Total time = 3xD/12000 + [200D-2xD]/12000
    Total time = (xD+200D)/12000

    And finally,
    Average speed = (total distance)/(total time)
    = D/[(xD+200D)/12000]
    = (12000D)/(xD+200D)
    = (12000)/(x+200)
    = E

    Cheers,
    Brent

    _________________
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    Thanked by: datonman
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    Post Wed Nov 04, 2015 10:26 am
    Hi datonman,

    This question can also be solved by TESTing VALUES.

    We're told that X% of a distance was spent traveling at 40 miles/hour while the rest of the distance was spent traveling at 60 miles/hour. We're asked for the AVERAGE SPEED for the entire trip.

    IF....
    Total Distance = 100 miles
    X = 40%

    40 miles was traveled at 40 miles/hour --> 1 hour of travel
    60 miles was traveled at 60 miles/hour --> 1 hour of travel

    Total Distance = (Av. Sp)(Total Time)
    100 miles = (Av. Sp.)(2 hours)
    100/2 = Av. Sp
    50 miles/hour = Av. Sp.

    So we're looking for an answer that equals 50 when X = 40....

    Answer A: (180-40)/2 = 70 NOT a match
    Answer B: (40+60)/4 = 25 NOT a match
    Answer C: (300-40)/5 = 52 NOT a match
    Answer D: 600/(115-40) = 8 NOT a match
    Answer E: 120000/(240) = 50 This IS a MATCH

    Final Answer: E

    GMAT assassins aren't born, they're made,
    Rich

    _________________
    Contact Rich at Rich.C@empowergmat.com

    Post Wed Nov 04, 2015 10:29 am
    Rich and I have demonstrated the two methods (Algebraic and Input-Output) for solving a question type I call Variables in the Answer Choices.
    If you'd like more information on these approaches, we have some free videos:
    - Variables in the Answer Choices - http://www.gmatprepnow.com/module/gmat-word-problems/video/933
    - Tips for the Algebraic Approach - http://www.gmatprepnow.com/module/gmat-word-problems/video/934
    - Tips for the Input-Output Approach - http://www.gmatprepnow.com/module/gmat-word-problems/video/935

    Cheers,
    Brent

    _________________
    Brent Hanneson – Founder of GMATPrepNow.com
    Use our video course along with Beat The GMAT's free 60-Day Study Guide

    Check out the online reviews of our course
    Come see all of our free resources

    GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!

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