Car average speed Problem

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mrigank_bhushan Just gettin' started! Default Avatar
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Car average speed Problem Post Mon Feb 03, 2014 5:12 pm
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  • Lap #[LAPCOUNT] ([LAPTIME])
    Someone Please help to solve this

    A car travels from Mayville to Rome at an average speed of 30 miles per hour and returns immediately along the same route at an average speed of 40 miles per hour. Of the following, which is closest to the average speed, in miles per hour, for the round-trip?

    (A) 32.0 (B) 33.0 (C) 34.3 (D) 35.5 (E) 36.5

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    Post Mon Feb 03, 2014 5:20 pm
    mrigank_bhushan wrote:
    Someone Please help to solve this

    A car travels from Mayville to Rome at an average speed of 30 miles per hour and returns immediately along the same route at an average speed of 40 miles per hour. Of the following, which is closest to the average speed, in miles per hour, for the round-trip?

    (A) 32.0 (B) 33.0 (C) 34.3 (D) 35.5 (E) 36.5
    We can solve this one quickly if we assign a "nice" distance between Mayville and Rome ("nice" means a distance that works well with 30 miles per hour AND 40 miles per hour)

    So, let's say the distance between Mayville and Rome = 120 miles

    Time = distance/speed
    So, time from Mayville and Rome (at 30 mph) = 120/30 = 4 hours
    Time from Rome to Mayville (at 40 mph) = 120/40 = 3 hours

    Average speed = (total distance traveled)/(total time)
    = (120 + 120)/(4 + 3)
    = 240/7
    = 34.something (if we use long division here, we'll stop once we get to the ones digit)
    = C

    Cheers.
    Brent

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    Post Tue Feb 04, 2014 1:00 am
    Hi mrigank_bhushan,

    Brent's solution is spot-on; it's exactly how I would solve the problem, so I won't rehash it here.

    It's worth noting that this type of "weighted average" question is a classic in the realm of standardized testing, so you will likely see something just like it on your Official GMAT. If you're given just the two speeds to work with, then pick a distance that works well with both speeds and do the necessary calculations. With a basic drawing and a bit of math, you'll have the correct answer.

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    Thanked by: manik11
    jesse tyler Just gettin' started! Default Avatar
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    Post Fri Jun 27, 2014 8:33 pm
    I find this post very interesting. Driving any vehicle also means thinking of your own and your passengers' safety. Abiding with the traffic rules is important to avoid any accidents and to have a safe trip.

    Post Fri Jun 27, 2014 10:57 pm
    Brent's method is ideal however an alternate method to solve the question of such type (constant distance and different speed)

    Average speed = 2 a*b / (a+b)

    = 2*30*40 / (30+40) = 34.3 ANSWER

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