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Math Help - Speed and Time problem

  1. #1
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    Speed and Time problem

    At 9 a.m., John was cycling from Point A to Point B. At the same time, Mary was cycling from Point B to Point A, using the same route as John. Cycling at 4km/hr faster than Mary, John would pass Mary 300m away from the midpoint.

    (a) What time did they pass each other?
    (b) If John took another 3 mins to reach Point B, what time would Mary reach Point A?



    Thank you for your help.
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  2. #2
    Super Member Bacterius's Avatar
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    Re: Speed and Time problem

    Try and visualize it. Since John moves faster than Mary, they will pass each other 300m beyond the midpoint (not before). Thus we get:

    J --------------------------- MIDPOINT ----- X ---------------------- M

    So this means, John has covered exactly 600m more distance than Mary, just by going 4km/h faster (do you see why? this is the key to solving this problem). Putting this into equations (600m = 0.6km, we are working in km/h here):

    V_{John} = V_{Mary} + 4
    D_{John} = D_{Mary} + 0.6

    Therefore using v = \frac{d}{t} we get:

    D_{John} = D_{Mary} + 4t
    D_{John} = D_{Mary} + 0.6

    Which simplifies to 4t = 0.6, thus t = 0.15 (hours). This is 9 minutes, therefore Mary and John will pass each other at 9:09am.

    By drawing a diagram, can you see how to solve question (b) now?

    EDIT: had made a mistake converting 0.15 to minutes... fixed now.
    Last edited by Bacterius; August 7th 2011 at 12:42 PM. Reason: 9 minutes, not 15
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  3. #3
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    Re: Speed and Time problem

    Thanks bacterius, I got (a) already can someone show me part (b)?

    I got 9:36 am, but the answer is 9:35am
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  4. #4
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    Re: Speed and Time problem

    .
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