Difficult Math Question #6

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800guy Master | Next Rank: 500 Posts Default Avatar
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Difficult Math Question #6

Post Thu Aug 31, 2006 6:19 pm
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  • Lap #[LAPCOUNT] ([LAPTIME])
    OA coming when a few people have answered...

    A and B ran a race of 480 m. In the first heat, A gives B a head start of 48 m and beats him by 1/10th of a minute. In the second heat, A gives B a head start of 144 m and is beaten by 1/30th of a minute. What is B's speed in m/s?
    (A) 12
    (B) 14
    (C) 16
    (D) 18
    (E) 20

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    bensanderson Newbie | Next Rank: 10 Posts Default Avatar
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    Post Fri Sep 01, 2006 7:32 am
    I'm glad you put this question up because I'm really not very good at rate/time/distance questions especially when they involve different variables, times, etc.

    My guess is that the answer is A, 12 m/s.

    At first I was trying to figure out what runner A's time (T) was but I couldn't get it to work. But since I knew that runner B's time was T-2 for 336 meters and T+6 for 432 meters, I thought that the difference between the heats for runner B would be 8 seconds. I know this a long way of doing this but I checked the answers to find out which rate would result in a difference of 8 seconds for the two different times. That's how I got A. The 336m run would take B 28 seconds and the 432m run would take B 36 seconds for a difference of 8 seconds.

    Is that correct? If not, please let me know. If it is correct, then is there a faster way to get the answer? Thanks for posting these questions.

    cheers.

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    marco Newbie | Next Rank: 10 Posts Default Avatar
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    Post Sun Sep 03, 2006 1:53 am
    First i do agree that the answer is 12

    but the only way i can think of speeding it up is as follows

    if for A B

    S=? S= ?
    T= t then T= t+6
    D= d D= 9d/10

    Now

    S=? S= ?
    T= t still but now T= t-2
    D= d still D= 7d/10 ( so if d =480 as we know
    then it is 7/10 x 480)

    now you have 2 equations for b which is what we are concerned with, Ai is only relative in this question

    so speed of B in firts heat will equal that in the second heat

    s=d/t 9d/10(t+6) = 7d/10(t-2)

    now solve for t which will = 30 sec

    and substitute back in the equation giving you an answer of 12m/s

    hope that helps

    piren Junior | Next Rank: 30 Posts Default Avatar
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    Post Tue Sep 05, 2006 12:23 am
    800guy wrote:
    OA coming when a few people have answered...

    A and B ran a race of 480 m. In the first heat, A gives B a head start of 48 m and beats him by 1/10th of a minute. In the second heat, A gives B a head start of 144 m and is beaten by 1/30th of a minute. What is B's speed in m/s?
    (A) 12
    (B) 14
    (C) 16
    (D) 18
    (E) 20
    Here's my solving method. Pay attention to units -- I suggest not to solve the 48-which is 10% of 480 and 144 (30%) until the very end.

    First race:
    A runs 480 m in t seconds
    B runs 0.9 x 480 m in t+6 seconds

    Second race:
    A runs 480 m in t seconds
    B runs 0.7 x 480 m in t-2 seconds

    Speeds of runners are presupposed constant between the two races
    which means that Sb1 = Sb2, where Sb1= speed of B in the first race and Sb2 = speed of B in the second race

    Speed= Distance / Time, hence

    Sb1 = 0.9 * 480 / (t+6)
    Sb2 = 0.7 * 480 / (t-2)

    Sb1 = Sb2 <=> 0.9*480 / (t+6) = 0.7*480 / (t-2)
    <=> 0.9*480*t - 1.8*480 = 0.7*480*t + 4,2*480
    <=> 0.9 t - 1.8 = 0.7 t + 4.2
    <=> 0.2 t = 6 <=> t = 30

    Plug in the value of t found in any of the formulas for Sb above: that leads us to

    Sb1 = 0.9 * 480 / (36) = 12 m / s

    Answer is A.

    800guy Master | Next Rank: 500 Posts Default Avatar
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    Post Tue Sep 05, 2006 7:43 pm
    OA:

    Ans: race 1 :- ta = tb-6 ( because A beats B by 6 sec)
    race 2 :- Ta = tb+2 ( because A looses to B by 2 sec)

    By the formula D= S * T
    we get two equations
    480/Sa = 432/Sb -6 ------------1)
    480/Sa = 336/Sb +2------------2)
    Equating these two equations we get Sb = 12
    ta,Sa stand for time taken by A and speed of A resp.

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    naveen1003 Junior | Next Rank: 30 Posts Default Avatar
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    Post Thu Jun 09, 2011 3:00 am
    Quote:
    A and B ran a race of 480 m. In the first heat, A gives B a head start of 48 m and beats him by 1/10th of a minute. In the second heat, A gives B a head start of 144 m and is beaten by 1/30th of a minute. What is B's speed in m/s?
    (A) 12
    (B) 14
    (C) 16
    (D) 18
    (E) 20
    distance = 480m = d
    B is given head start of 48 meters (which is 10% of 480) or we can say that B travels .9d
    time taken by A = t sec and thus time taken by B = t+6 (=1/10 of a minute = 6 seconds)
    B is given head start of 144 meters (30% of 480) or B travels .7d
    time taken by A = t sec and time taken by B = t-2 (B beats A by 1/30 of a minute which is 2 seconds)
    speed of B = distance/time = (.9d)/(t+6) = (.7d)/(t-2)
    9t-18 = 7t + 42
    => t=30
    Thus speed of B = .9d/(t+6) = .9*480/36 = 12 m/sec

    Post Thu Jun 09, 2011 5:44 am
    800guy wrote:
    OA coming when a few people have answered...

    A and B ran a race of 480 m. In the first heat, A gives B a head start of 48 m and beats him by 1/10th of a minute. In the second heat, A gives B a head start of 144 m and is beaten by 1/30th of a minute. What is B�s speed in m/s?
    (A) 12
    (B) 14
    (C) 16
    (D) 18
    (E) 20
    We can plug in the answers, which represent B's rate.
    The correct answer must be a factor of 480.
    Eliminate B and D.

    In the first heat, A beats B by (1/10)*60 = 6 seconds.
    In the second heat, B beats A by (1/30)*60 = 2 seconds.

    Answer choice C: B = 16 meters per second.
    First heat:
    Time for B = d/r = 480/16 = 30 seconds.
    Headstart given to A = 48/16 = 3 seconds.
    Since A beats B by 6 seconds, total time for A = 30-(3+6) = 21 seconds.
    21 is not a factor of 480.
    Eliminate C.

    Answer choice A: B = 12 meters per second.
    First heat:
    Time for B = d/r = 480/12 = 40 seconds.
    Headstart given to A = 48/12 = 4 seconds.
    Since A beats B by 6 seconds, total time for A = 40-(4+6) = 30 seconds.
    Rate for A = d/t = 480/30 = 16 meters per second.

    Second heat:
    Headstart given to B = 144/12 = 12 seconds.
    From the first heat: Time for B - Time for A = 40-30 = 10 seconds.
    Since B is given a 12-second headstart, and the time for A is only 10 seconds less than the time for B, B beats A by 12-10 = 2 seconds.
    Success!

    The correct answer is A.

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    Vish_ Junior | Next Rank: 30 Posts Default Avatar
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    Post Thu Jun 09, 2011 6:52 am
    IMO A

    sunilramu Junior | Next Rank: 30 Posts Default Avatar
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    Post Thu Jun 09, 2011 4:46 pm
    Mitch,

    Can you please elaborate on how you arrived at the premise that speeds of both A and B should to be factors of 480.

    Thanks

    Post Thu Jun 09, 2011 5:00 pm
    sunilramu wrote:
    Mitch,

    Can you please elaborate on how you arrived at the premise that speeds of both A and B should to be factors of 480.

    Thanks
    When the given times are converted into seconds, the results are integers:
    1/10 of a minute = 6 seconds.
    1/30 of a minute = 2 seconds.

    Thus, the correct rate for B almost certainly will be a factor of the distance; otherwise, the resulting times will not be integer values.
    Since the distance is 480, the correct answer should be a factor of 480.

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