Algebra Puzzle Question

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Julia drives to her holiday destination over a period of five days. On the first day she travels a certain distance, on the second day she travels half that distance, on the third day a third of that distance, on the fourth day one quarter of the distance and on the fifth day one fifth of the distance. If her destination is $1000$ km away, write an equation and solve it to find how far she travels on the first day to the nearest kilometre.




A textbook question from my exercise. The textbook solution is $438$ km.



My attempt



Let distance travelled on the first day $= x$



Then



$x+x/2+x/6+x/24+x/120=1000$



$(103/60)x=1000$



$x=583$



Therefore distance travelled on the first day is $583$ km.



Is the mistake in my working or is the textbook solution provided incorrect?




algebra-precalculus




share|cite|improve this question





















  • Why downvoting?
    – Robert Z
    Aug 6 at 7:50










  • I dont understand ?
    – Nicolas
    Aug 6 at 7:51










  • I suppose, from my first impression, that distance is always referring to the distance made on the first day
    – dEmigOd
    Aug 6 at 7:54






  • 3




    The "distance" is always the one of the first day (not the distance of the previous day). Therefore the equation should be $x+x/2+x/3+x/4+x/5=1000$
    – Robert Z
    Aug 6 at 7:54











  • So where is the error in my working?
    – Nicolas
    Aug 6 at 7:56














up vote
0
down vote

favorite













Julia drives to her holiday destination over a period of five days. On the first day she travels a certain distance, on the second day she travels half that distance, on the third day a third of that distance, on the fourth day one quarter of the distance and on the fifth day one fifth of the distance. If her destination is $1000$ km away, write an equation and solve it to find how far she travels on the first day to the nearest kilometre.




A textbook question from my exercise. The textbook solution is $438$ km.



My attempt



Let distance travelled on the first day $= x$



Then



$x+x/2+x/6+x/24+x/120=1000$



$(103/60)x=1000$



$x=583$



Therefore distance travelled on the first day is $583$ km.



Is the mistake in my working or is the textbook solution provided incorrect?




algebra-precalculus




share|cite|improve this question





















  • Why downvoting?
    – Robert Z
    Aug 6 at 7:50










  • I dont understand ?
    – Nicolas
    Aug 6 at 7:51










  • I suppose, from my first impression, that distance is always referring to the distance made on the first day
    – dEmigOd
    Aug 6 at 7:54






  • 3




    The "distance" is always the one of the first day (not the distance of the previous day). Therefore the equation should be $x+x/2+x/3+x/4+x/5=1000$
    – Robert Z
    Aug 6 at 7:54











  • So where is the error in my working?
    – Nicolas
    Aug 6 at 7:56












up vote
0
down vote

favorite









up vote
0
down vote

favorite












Julia drives to her holiday destination over a period of five days. On the first day she travels a certain distance, on the second day she travels half that distance, on the third day a third of that distance, on the fourth day one quarter of the distance and on the fifth day one fifth of the distance. If her destination is $1000$ km away, write an equation and solve it to find how far she travels on the first day to the nearest kilometre.




A textbook question from my exercise. The textbook solution is $438$ km.



My attempt



Let distance travelled on the first day $= x$



Then



$x+x/2+x/6+x/24+x/120=1000$



$(103/60)x=1000$



$x=583$



Therefore distance travelled on the first day is $583$ km.



Is the mistake in my working or is the textbook solution provided incorrect?




algebra-precalculus




share|cite|improve this question














Julia drives to her holiday destination over a period of five days. On the first day she travels a certain distance, on the second day she travels half that distance, on the third day a third of that distance, on the fourth day one quarter of the distance and on the fifth day one fifth of the distance. If her destination is $1000$ km away, write an equation and solve it to find how far she travels on the first day to the nearest kilometre.




A textbook question from my exercise. The textbook solution is $438$ km.



My attempt



Let distance travelled on the first day $= x$



Then



$x+x/2+x/6+x/24+x/120=1000$



$(103/60)x=1000$



$x=583$



Therefore distance travelled on the first day is $583$ km.



Is the mistake in my working or is the textbook solution provided incorrect?





algebra-precalculus





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Aug 6 at 8:04









TheSimpliFire

9,69261952




9,69261952









asked Aug 6 at 7:49









Nicolas

344




344











  • Why downvoting?
    – Robert Z
    Aug 6 at 7:50










  • I dont understand ?
    – Nicolas
    Aug 6 at 7:51










  • I suppose, from my first impression, that distance is always referring to the distance made on the first day
    – dEmigOd
    Aug 6 at 7:54






  • 3




    The "distance" is always the one of the first day (not the distance of the previous day). Therefore the equation should be $x+x/2+x/3+x/4+x/5=1000$
    – Robert Z
    Aug 6 at 7:54











  • So where is the error in my working?
    – Nicolas
    Aug 6 at 7:56
















  • Why downvoting?
    – Robert Z
    Aug 6 at 7:50










  • I dont understand ?
    – Nicolas
    Aug 6 at 7:51










  • I suppose, from my first impression, that distance is always referring to the distance made on the first day
    – dEmigOd
    Aug 6 at 7:54






  • 3




    The "distance" is always the one of the first day (not the distance of the previous day). Therefore the equation should be $x+x/2+x/3+x/4+x/5=1000$
    – Robert Z
    Aug 6 at 7:54











  • So where is the error in my working?
    – Nicolas
    Aug 6 at 7:56















Why downvoting?
– Robert Z
Aug 6 at 7:50




Why downvoting?
– Robert Z
Aug 6 at 7:50












I dont understand ?
– Nicolas
Aug 6 at 7:51




I dont understand ?
– Nicolas
Aug 6 at 7:51












I suppose, from my first impression, that distance is always referring to the distance made on the first day
– dEmigOd
Aug 6 at 7:54




I suppose, from my first impression, that distance is always referring to the distance made on the first day
– dEmigOd
Aug 6 at 7:54




3




3




The "distance" is always the one of the first day (not the distance of the previous day). Therefore the equation should be $x+x/2+x/3+x/4+x/5=1000$
– Robert Z
Aug 6 at 7:54





The "distance" is always the one of the first day (not the distance of the previous day). Therefore the equation should be $x+x/2+x/3+x/4+x/5=1000$
– Robert Z
Aug 6 at 7:54













So where is the error in my working?
– Nicolas
Aug 6 at 7:56




So where is the error in my working?
– Nicolas
Aug 6 at 7:56










2 Answers
2






active

oldest

votes

















up vote
0
down vote



accepted










$$x+x/2+x/3+x/4+x/5=1000$$



$$x=437.95$$



I think now you will understand where you mistaken.



Hope it will help you.



Nice attempt.






share|cite|improve this answer























  • Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
    – José Carlos Santos
    Aug 6 at 8:01

















up vote
0
down vote













There is an ambiguity in the question when it talks about that distance in. e.g. "on the third day a third of that distance" ... is 'that distance' referring to the distance of the previous day, or is the phrase always referring to the distance of the very first day? You interpreted the phrase in the former way, but the book interpreted it in the latter way.






share|cite|improve this answer





















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    2 Answers
    2






    active

    oldest

    votes








    2 Answers
    2






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes








    up vote
    0
    down vote



    accepted










    $$x+x/2+x/3+x/4+x/5=1000$$



    $$x=437.95$$



    I think now you will understand where you mistaken.



    Hope it will help you.



    Nice attempt.






    share|cite|improve this answer























    • Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
      – José Carlos Santos
      Aug 6 at 8:01














    up vote
    0
    down vote



    accepted










    $$x+x/2+x/3+x/4+x/5=1000$$



    $$x=437.95$$



    I think now you will understand where you mistaken.



    Hope it will help you.



    Nice attempt.






    share|cite|improve this answer























    • Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
      – José Carlos Santos
      Aug 6 at 8:01












    up vote
    0
    down vote



    accepted







    up vote
    0
    down vote



    accepted






    $$x+x/2+x/3+x/4+x/5=1000$$



    $$x=437.95$$



    I think now you will understand where you mistaken.



    Hope it will help you.



    Nice attempt.






    share|cite|improve this answer















    $$x+x/2+x/3+x/4+x/5=1000$$



    $$x=437.95$$



    I think now you will understand where you mistaken.



    Hope it will help you.



    Nice attempt.







    share|cite|improve this answer















    share|cite|improve this answer



    share|cite|improve this answer








    edited Aug 6 at 8:04









    TheSimpliFire

    9,69261952




    9,69261952











    answered Aug 6 at 7:58









    neh

    163




    163











    • Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
      – José Carlos Santos
      Aug 6 at 8:01
















    • Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
      – José Carlos Santos
      Aug 6 at 8:01















    Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
    – José Carlos Santos
    Aug 6 at 8:01




    Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
    – José Carlos Santos
    Aug 6 at 8:01










    up vote
    0
    down vote













    There is an ambiguity in the question when it talks about that distance in. e.g. "on the third day a third of that distance" ... is 'that distance' referring to the distance of the previous day, or is the phrase always referring to the distance of the very first day? You interpreted the phrase in the former way, but the book interpreted it in the latter way.






    share|cite|improve this answer

























      up vote
      0
      down vote













      There is an ambiguity in the question when it talks about that distance in. e.g. "on the third day a third of that distance" ... is 'that distance' referring to the distance of the previous day, or is the phrase always referring to the distance of the very first day? You interpreted the phrase in the former way, but the book interpreted it in the latter way.






      share|cite|improve this answer























        up vote
        0
        down vote










        up vote
        0
        down vote









        There is an ambiguity in the question when it talks about that distance in. e.g. "on the third day a third of that distance" ... is 'that distance' referring to the distance of the previous day, or is the phrase always referring to the distance of the very first day? You interpreted the phrase in the former way, but the book interpreted it in the latter way.






        share|cite|improve this answer













        There is an ambiguity in the question when it talks about that distance in. e.g. "on the third day a third of that distance" ... is 'that distance' referring to the distance of the previous day, or is the phrase always referring to the distance of the very first day? You interpreted the phrase in the former way, but the book interpreted it in the latter way.







        share|cite|improve this answer













        share|cite|improve this answer



        share|cite|improve this answer











        answered Aug 6 at 10:55









        Bram28

        55.2k33982




        55.2k33982






















             

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