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  1. MHB Apprentice

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    #1
    Joan is riding her bicycle along a track at 15 miles per hour. Anthony, who is ahead of Joan on the same track, is riding his bicycle at 12 miles per hour. If it will take Joan 5 hours to catch Anthony at their current speeds, how many mile ahead of Joan on the track is Anthony?

    How would you solve it using the d=rt formula?

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    #2
    Quote Originally Posted by 816318 View Post
    Joan is riding her bicycle along a track at 15 miles per hour. Anthony, who is ahead of Joan on the same track, is riding his bicycle at 12 miles per hour. If it will take Joan 5 hours to catch Anthony at their current speeds, how many mile ahead of Joan on the track is Anthony?

    How would you solve it using the d=rt formula?
    Hi 816318, could you expand on what you intend the d = rt formula to mean? Maybe i should know from experience.. I'm thinking distance equals something by time.. Ha . I'll feel silly when i realise, but we have to know for sure!

  3. Pessimist Singularitarian
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    #3
    Quote Originally Posted by 816318 View Post
    Joan is riding her bicycle along a track at 15 miles per hour. Anthony, who is ahead of Joan on the same track, is riding his bicycle at 12 miles per hour. If it will take Joan 5 hours to catch Anthony at their current speeds, how many mile ahead of Joan on the track is Anthony?

    How would you solve it using the d=rt formula?
    We can simplify this problem a bit if we orient our coordinate axis such that Anthony is at the origin and Joan is some distance away approaching the origin at 3 mph. Can you proceed?

  4. MHB Apprentice

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    Quote Originally Posted by MarkFL View Post
    We can simplify this problem a bit if we orient our coordinate axis such that Anthony is at the origin and Joan is some distance away approaching the origin at 3 mph. Can you proceed?
    Thanks I got it now, d=3(5) 15!

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    #5
    Another approach would be to initially put Joan at the origin and Anthony at $d$. Disnaces are in miles and time in hours. And then:

    Joan's position as a function of time is:

    $ \displaystyle J(t)=15t$

    Anthony's position as a function of time is:

    $ \displaystyle A(t)=12t+d$

    Now, we are told they meet in 5 hours, or:

    $ \displaystyle J(5)=A(5)$

    $ \displaystyle 15(5)=12(5)+d$

    $ \displaystyle d=15(5)-12(5)=3(5)(5-4)=15$

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    #6
    Quote Originally Posted by Joppy View Post
    Hi 816318, could you expand on what you intend the d = rt formula to mean? Maybe i should know from experience.. I'm thinking distance equals something by time.. Ha . I'll feel silly when i realise, but we have to know for sure!
    distance traveled= rate of travel times time traveled.

    You may know it better as "d= vt" where "v" is now "velocity".

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