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Math Help - Race word problem

  1. #1
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    Sep 2008
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    Race word problem

    At a recent world cup 10000m speed skating race, the winner, A, finished in 13 minutes 20.4 seconds. The last place finisher, B, took 15 minutes 37.0 seconds. The track is 400 m long.
    i. How many meters did B still have to run when A finished?
    ii. How far had A run when he first overlapped B?
    iii. How many times was B lapped?

    10000m/400m= 25 laps
    A= 800.4 seconds/25 laps = 32.016 seconds/lap
    B=937 seconds/25 laps = 37.48 seconds /lap

    i. 37.48seconds/1lap=800.4seconds/x
    x=8542.2
    B had 8542.2 meters done when A finished, so B had 10000-8542.2=1457.8 left to go.

    I would like help on parts ii & iii because I am not sure how to set up the equation where A's distance =B's distance. nor can I figure out how to tell how many times B was lapped.
    My guess is that you set the velocity and time of A equal to the velocity of b and solve for the time but I'm not sure.
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  2. #2
    MHF Contributor
    Joined
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    The first part is okay.

    ii. How far had A run when he first overlapped B?
    Rate of A = 10,000 /800.4 = 12.49375 m/sec
    Rate of B = 10,000 /937 = 10.67236 m/sec

    A had run 1 more lap than B when he overtook B, so,
    12.49375(t) = 10.67236(t) +400
    t = 400 /(12.49375 -10.67236) = 219.61249 sec.
    Hence, A ran
    (12.49375 m/sec)(219.61249 sec) = 2743.78 meters -------answer.
    ... when he caught up with B for the first time

    ----------------------
    iii. How many times was B lapped?

    From part (ii) above, A overlapped B every 2743.78 meters, so,
    10,000 /2743.78 = 3.6446
    Meaning, A overlapped B, 3 times --------------answer.
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  3. #3
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    Sep 2008
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    thank you very much. I wish I would have got that myself.
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