For what values of t, $20tequiv15t pmod {0.5}$?












0












$begingroup$


The question is: There is a race on a circular track of length $0.5$ km. The race is $4$ km. Two people start at the same point with speeds $20$ m/s and $10$ m/s respectively. Find the distance covered by the first person when they meet the second person for the third time.



My formulation of the question was, $20tequiv15t pmod{0.5}$, where $t$ is time elapsed. However, I have no idea how to solve these type of equations.






modular-arithmetic







share|cite|improve this question











$endgroup$












  • $begingroup$
    The track length is measured in km, and their speeds in mph. Is that intentional?
    $endgroup$
    – Arthur
    Dec 18 '18 at 15:34










  • $begingroup$
    @Arthur Yup, I just checked. Can't we just convert 4Km to 4000m? Their speeds are in meters per second. I accidentally wrote hour
    $endgroup$
    – Ryder Rude
    Dec 18 '18 at 15:37












  • $begingroup$
    m/s makes much more sense than miles per hour. That being said, I don't think much conversion is needed. The only really important numbers here are that one runner is twice as fast as the other, and the track is 500m long (which is a very odd length for a running track, now that I think about it; the standard is 400m). And 20m/s is insanely fast (twice the speed of any world class 100m dasher). Math problems aren't always thought through, I guess.
    $endgroup$
    – Arthur
    Dec 18 '18 at 15:56












  • $begingroup$
    @RyderRude $20t equiv 10t( mod{500})$ is easier to look at right?
    $endgroup$
    – 1.414212
    Dec 18 '18 at 17:31


















0












$begingroup$


The question is: There is a race on a circular track of length $0.5$ km. The race is $4$ km. Two people start at the same point with speeds $20$ m/s and $10$ m/s respectively. Find the distance covered by the first person when they meet the second person for the third time.



My formulation of the question was, $20tequiv15t pmod{0.5}$, where $t$ is time elapsed. However, I have no idea how to solve these type of equations.






modular-arithmetic







share|cite|improve this question











$endgroup$












  • $begingroup$
    The track length is measured in km, and their speeds in mph. Is that intentional?
    $endgroup$
    – Arthur
    Dec 18 '18 at 15:34










  • $begingroup$
    @Arthur Yup, I just checked. Can't we just convert 4Km to 4000m? Their speeds are in meters per second. I accidentally wrote hour
    $endgroup$
    – Ryder Rude
    Dec 18 '18 at 15:37












  • $begingroup$
    m/s makes much more sense than miles per hour. That being said, I don't think much conversion is needed. The only really important numbers here are that one runner is twice as fast as the other, and the track is 500m long (which is a very odd length for a running track, now that I think about it; the standard is 400m). And 20m/s is insanely fast (twice the speed of any world class 100m dasher). Math problems aren't always thought through, I guess.
    $endgroup$
    – Arthur
    Dec 18 '18 at 15:56












  • $begingroup$
    @RyderRude $20t equiv 10t( mod{500})$ is easier to look at right?
    $endgroup$
    – 1.414212
    Dec 18 '18 at 17:31
















0












0








0





$begingroup$


The question is: There is a race on a circular track of length $0.5$ km. The race is $4$ km. Two people start at the same point with speeds $20$ m/s and $10$ m/s respectively. Find the distance covered by the first person when they meet the second person for the third time.



My formulation of the question was, $20tequiv15t pmod{0.5}$, where $t$ is time elapsed. However, I have no idea how to solve these type of equations.






modular-arithmetic







share|cite|improve this question











$endgroup$




The question is: There is a race on a circular track of length $0.5$ km. The race is $4$ km. Two people start at the same point with speeds $20$ m/s and $10$ m/s respectively. Find the distance covered by the first person when they meet the second person for the third time.



My formulation of the question was, $20tequiv15t pmod{0.5}$, where $t$ is time elapsed. However, I have no idea how to solve these type of equations.






modular-arithmetic




modular-arithmetic






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 18 '18 at 16:18









Brahadeesh

6,42442363




6,42442363










asked Dec 18 '18 at 15:29









Ryder RudeRyder Rude

412111




412111












  • $begingroup$
    The track length is measured in km, and their speeds in mph. Is that intentional?
    $endgroup$
    – Arthur
    Dec 18 '18 at 15:34










  • $begingroup$
    @Arthur Yup, I just checked. Can't we just convert 4Km to 4000m? Their speeds are in meters per second. I accidentally wrote hour
    $endgroup$
    – Ryder Rude
    Dec 18 '18 at 15:37












  • $begingroup$
    m/s makes much more sense than miles per hour. That being said, I don't think much conversion is needed. The only really important numbers here are that one runner is twice as fast as the other, and the track is 500m long (which is a very odd length for a running track, now that I think about it; the standard is 400m). And 20m/s is insanely fast (twice the speed of any world class 100m dasher). Math problems aren't always thought through, I guess.
    $endgroup$
    – Arthur
    Dec 18 '18 at 15:56












  • $begingroup$
    @RyderRude $20t equiv 10t( mod{500})$ is easier to look at right?
    $endgroup$
    – 1.414212
    Dec 18 '18 at 17:31




















  • $begingroup$
    The track length is measured in km, and their speeds in mph. Is that intentional?
    $endgroup$
    – Arthur
    Dec 18 '18 at 15:34










  • $begingroup$
    @Arthur Yup, I just checked. Can't we just convert 4Km to 4000m? Their speeds are in meters per second. I accidentally wrote hour
    $endgroup$
    – Ryder Rude
    Dec 18 '18 at 15:37












  • $begingroup$
    m/s makes much more sense than miles per hour. That being said, I don't think much conversion is needed. The only really important numbers here are that one runner is twice as fast as the other, and the track is 500m long (which is a very odd length for a running track, now that I think about it; the standard is 400m). And 20m/s is insanely fast (twice the speed of any world class 100m dasher). Math problems aren't always thought through, I guess.
    $endgroup$
    – Arthur
    Dec 18 '18 at 15:56












  • $begingroup$
    @RyderRude $20t equiv 10t( mod{500})$ is easier to look at right?
    $endgroup$
    – 1.414212
    Dec 18 '18 at 17:31


















$begingroup$
The track length is measured in km, and their speeds in mph. Is that intentional?
$endgroup$
– Arthur
Dec 18 '18 at 15:34




$begingroup$
The track length is measured in km, and their speeds in mph. Is that intentional?
$endgroup$
– Arthur
Dec 18 '18 at 15:34












$begingroup$
@Arthur Yup, I just checked. Can't we just convert 4Km to 4000m? Their speeds are in meters per second. I accidentally wrote hour
$endgroup$
– Ryder Rude
Dec 18 '18 at 15:37






$begingroup$
@Arthur Yup, I just checked. Can't we just convert 4Km to 4000m? Their speeds are in meters per second. I accidentally wrote hour
$endgroup$
– Ryder Rude
Dec 18 '18 at 15:37














$begingroup$
m/s makes much more sense than miles per hour. That being said, I don't think much conversion is needed. The only really important numbers here are that one runner is twice as fast as the other, and the track is 500m long (which is a very odd length for a running track, now that I think about it; the standard is 400m). And 20m/s is insanely fast (twice the speed of any world class 100m dasher). Math problems aren't always thought through, I guess.
$endgroup$
– Arthur
Dec 18 '18 at 15:56






$begingroup$
m/s makes much more sense than miles per hour. That being said, I don't think much conversion is needed. The only really important numbers here are that one runner is twice as fast as the other, and the track is 500m long (which is a very odd length for a running track, now that I think about it; the standard is 400m). And 20m/s is insanely fast (twice the speed of any world class 100m dasher). Math problems aren't always thought through, I guess.
$endgroup$
– Arthur
Dec 18 '18 at 15:56














$begingroup$
@RyderRude $20t equiv 10t( mod{500})$ is easier to look at right?
$endgroup$
– 1.414212
Dec 18 '18 at 17:31






$begingroup$
@RyderRude $20t equiv 10t( mod{500})$ is easier to look at right?
$endgroup$
– 1.414212
Dec 18 '18 at 17:31












1 Answer
1






active

oldest

votes


















3












$begingroup$

Once you correct $.5 km = 500m$



We have $20t equiv 15t pmod {500}$



So $5t equiv 0 pmod {500}$



When confused. Go back to something less confusing.



$5tequiv 0 pmod {500}$



so there is an integer $k$ so that



$5t = 500k$



$t = 100k$



$t$ being any multiple of $100$ seconds will do.



For example: After $100$ seconds, runner 1 will have ran $2000 m$ or or $2 km$ or $4$ laps. Will runner 2 will have run $1500 m$ or $1.5 km$ or $3$ laps.






share|cite|improve this answer









$endgroup$













    Your Answer





    StackExchange.ifUsing("editor", function () {
    return StackExchange.using("mathjaxEditing", function () {
    StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
    StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
    });
    });
    }, "mathjax-editing");

    StackExchange.ready(function() {
    var channelOptions = {
    tags: "".split(" "),
    id: "69"
    };
    initTagRenderer("".split(" "), "".split(" "), channelOptions);

    StackExchange.using("externalEditor", function() {
    // Have to fire editor after snippets, if snippets enabled
    if (StackExchange.settings.snippets.snippetsEnabled) {
    StackExchange.using("snippets", function() {
    createEditor();
    });
    }
    else {
    createEditor();
    }
    });

    function createEditor() {
    StackExchange.prepareEditor({
    heartbeatType: 'answer',
    autoActivateHeartbeat: false,
    convertImagesToLinks: true,
    noModals: true,
    showLowRepImageUploadWarning: true,
    reputationToPostImages: 10,
    bindNavPrevention: true,
    postfix: "",
    imageUploader: {
    brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
    contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
    allowUrls: true
    },
    noCode: true, onDemand: true,
    discardSelector: ".discard-answer"
    ,immediatelyShowMarkdownHelp:true
    });


    }
    });














    draft saved

    draft discarded


















    StackExchange.ready(
    function () {
    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3045289%2ffor-what-values-of-t-20t-equiv15t-pmod-0-5%23new-answer', 'question_page');
    }
    );

    Post as a guest















    Required, but never shown

























    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    3












    $begingroup$

    Once you correct $.5 km = 500m$



    We have $20t equiv 15t pmod {500}$



    So $5t equiv 0 pmod {500}$



    When confused. Go back to something less confusing.



    $5tequiv 0 pmod {500}$



    so there is an integer $k$ so that



    $5t = 500k$



    $t = 100k$



    $t$ being any multiple of $100$ seconds will do.



    For example: After $100$ seconds, runner 1 will have ran $2000 m$ or or $2 km$ or $4$ laps. Will runner 2 will have run $1500 m$ or $1.5 km$ or $3$ laps.






    share|cite|improve this answer









    $endgroup$


















      3












      $begingroup$

      Once you correct $.5 km = 500m$



      We have $20t equiv 15t pmod {500}$



      So $5t equiv 0 pmod {500}$



      When confused. Go back to something less confusing.



      $5tequiv 0 pmod {500}$



      so there is an integer $k$ so that



      $5t = 500k$



      $t = 100k$



      $t$ being any multiple of $100$ seconds will do.



      For example: After $100$ seconds, runner 1 will have ran $2000 m$ or or $2 km$ or $4$ laps. Will runner 2 will have run $1500 m$ or $1.5 km$ or $3$ laps.






      share|cite|improve this answer









      $endgroup$
















        3












        3








        3





        $begingroup$

        Once you correct $.5 km = 500m$



        We have $20t equiv 15t pmod {500}$



        So $5t equiv 0 pmod {500}$



        When confused. Go back to something less confusing.



        $5tequiv 0 pmod {500}$



        so there is an integer $k$ so that



        $5t = 500k$



        $t = 100k$



        $t$ being any multiple of $100$ seconds will do.



        For example: After $100$ seconds, runner 1 will have ran $2000 m$ or or $2 km$ or $4$ laps. Will runner 2 will have run $1500 m$ or $1.5 km$ or $3$ laps.






        share|cite|improve this answer









        $endgroup$



        Once you correct $.5 km = 500m$



        We have $20t equiv 15t pmod {500}$



        So $5t equiv 0 pmod {500}$



        When confused. Go back to something less confusing.



        $5tequiv 0 pmod {500}$



        so there is an integer $k$ so that



        $5t = 500k$



        $t = 100k$



        $t$ being any multiple of $100$ seconds will do.



        For example: After $100$ seconds, runner 1 will have ran $2000 m$ or or $2 km$ or $4$ laps. Will runner 2 will have run $1500 m$ or $1.5 km$ or $3$ laps.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Dec 18 '18 at 17:51









        fleabloodfleablood

        71.5k22686




        71.5k22686






























            draft saved

            draft discarded




















































            Thanks for contributing an answer to Mathematics Stack Exchange!


            • Please be sure to answer the question. Provide details and share your research!

            But avoid …



            • Asking for help, clarification, or responding to other answers.

            • Making statements based on opinion; back them up with references or personal experience.


            Use MathJax to format equations. MathJax reference.


            To learn more, see our tips on writing great answers.




            draft saved


            draft discarded














            StackExchange.ready(
            function () {
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3045289%2ffor-what-values-of-t-20t-equiv15t-pmod-0-5%23new-answer', 'question_page');
            }
            );

            Post as a guest















            Required, but never shown





















































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown

































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown







            -

            Popular posts from this blog

            Probability when a professor distributes a quiz and homework assignment to a class of n students.

            Image
            0 0 $begingroup$ Need help with this problem. Suppose our lazy professor collects a quiz and a homework assignment from a class of n students one day, then distributes both the quizzes and the homework assignments back to the class in a random fashion for grading. Each student receives one quiz and one homework assignment to grade. (a) What is the probability that every student receives someone else's quiz to grade, and someone else's homework to grade? (b) What is the probability that no student receives both their own quiz and their own homework assignment to grade? In this case, some students may receive their own quiz, and others may receive their own homework assignment. (c) Compute the limiting probability as n approaches infinity in each case. ...
            Read more

            Aardman Animations

            Image
            Aardman Animations, Ltd. Aardman Animations Tipo privada Atividade Animação em stop-motion , Animação em CGI Fundação 1972 Fundador(es) Peter Lord David Sproxton Sede Bristol, Inglaterra  Reino Unido Proprietário(s) Dreamworks Pessoas-chave Peter Lord David Sproxton Nick Park Divisões Aardman Features Aardman Digital Aardman Commercials Aardman Broadcast Aardman International Aardman Rights Aardman Effects Aardman 3-D Systems Aardman Nathan Love AardBoiled Website oficial aardman.com ...
            Read more

            Are they similar matrix

            Image
            0 $begingroup$ Do $begin{bmatrix} 0&i&0\0&0&1\0&0&0 end{bmatrix} $ and $begin{bmatrix} 0&0&0\-i&0&0\0&1&0 end{bmatrix} $ are similar.Is this True/false Clearly both are nilpotent and one is conjucate transpose of other but how to know if they are similar.i'm stuck. Please help me linear-algebra vector-spaces eigenvalues-eigenvectors generalizedeigenvector share | cite | improve this question edited Dec 10 '18 at 6:38 Vasanth Kris asked Dec 10 '18 at 6:19 ...
            Read more