Ratio of Speeds of Trains

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Recently, I came across a question:




A train $T_1$ from station $P$ to $Q$, and, the other train $T_2$ from station $Q$ to $P$, start simultaneously. After they meet, the trains reach their destinations after $9$ hours and $16$ hours respectively. The ratio of their speeds is ___.

(i) $2:3$

(ii) $4:3$

(iii) $6:7$

(iv) $9:16$




The only formula I remembered was
$$
textSpeed = fractextDistancetextTime cdotp
$$
I couldn't solve the question. It became more and more complex when I tried using this formula directly. Later I found out that the correct answer is (ii) $4:3$. The only explanation given was $sqrt16:sqrt9$. I can't understand how
$$
sqrtoperatornameTime(T_2) : sqrtoperatornameTime(T_1)
$$
is the right formula to solve such kind of questions?







share|cite|improve this question






















  • Related to this question.
    – Bill Wallis
    Aug 24 at 10:21






  • 1




    Trying to memorize formulas in order to solve math problems will not get you far. The times the trains needed to reach their destinations were $t+9$ and $t+16$ respectively, $t$ is the time when they met. You know that the distance they traveled was the same, can you figure out the result?
    – tst
    Aug 24 at 10:23











  • To expand on what @tst is saying, if you tried to remember formulas for every question like this, there would be a lot of formulas, and trying to decide which one is appropriate in each case would be a nightmare. It's much better to know a few, really important formulas (like $textspeed = fractextdistancetexttime$) and then derive the formula you need for any other problem using those, use the new formula you just derived, then forget about it.
    – Arthur
    Aug 24 at 10:43











  • @tst I totally agree. That's why I asked the question here to understand how the formula actually works!
    – code_master5
    Aug 25 at 13:01














up vote
0
down vote

favorite












Recently, I came across a question:




A train $T_1$ from station $P$ to $Q$, and, the other train $T_2$ from station $Q$ to $P$, start simultaneously. After they meet, the trains reach their destinations after $9$ hours and $16$ hours respectively. The ratio of their speeds is ___.

(i) $2:3$

(ii) $4:3$

(iii) $6:7$

(iv) $9:16$




The only formula I remembered was
$$
textSpeed = fractextDistancetextTime cdotp
$$
I couldn't solve the question. It became more and more complex when I tried using this formula directly. Later I found out that the correct answer is (ii) $4:3$. The only explanation given was $sqrt16:sqrt9$. I can't understand how
$$
sqrtoperatornameTime(T_2) : sqrtoperatornameTime(T_1)
$$
is the right formula to solve such kind of questions?







share|cite|improve this question






















  • Related to this question.
    – Bill Wallis
    Aug 24 at 10:21






  • 1




    Trying to memorize formulas in order to solve math problems will not get you far. The times the trains needed to reach their destinations were $t+9$ and $t+16$ respectively, $t$ is the time when they met. You know that the distance they traveled was the same, can you figure out the result?
    – tst
    Aug 24 at 10:23











  • To expand on what @tst is saying, if you tried to remember formulas for every question like this, there would be a lot of formulas, and trying to decide which one is appropriate in each case would be a nightmare. It's much better to know a few, really important formulas (like $textspeed = fractextdistancetexttime$) and then derive the formula you need for any other problem using those, use the new formula you just derived, then forget about it.
    – Arthur
    Aug 24 at 10:43











  • @tst I totally agree. That's why I asked the question here to understand how the formula actually works!
    – code_master5
    Aug 25 at 13:01












up vote
0
down vote

favorite









up vote
0
down vote

favorite











Recently, I came across a question:




A train $T_1$ from station $P$ to $Q$, and, the other train $T_2$ from station $Q$ to $P$, start simultaneously. After they meet, the trains reach their destinations after $9$ hours and $16$ hours respectively. The ratio of their speeds is ___.

(i) $2:3$

(ii) $4:3$

(iii) $6:7$

(iv) $9:16$




The only formula I remembered was
$$
textSpeed = fractextDistancetextTime cdotp
$$
I couldn't solve the question. It became more and more complex when I tried using this formula directly. Later I found out that the correct answer is (ii) $4:3$. The only explanation given was $sqrt16:sqrt9$. I can't understand how
$$
sqrtoperatornameTime(T_2) : sqrtoperatornameTime(T_1)
$$
is the right formula to solve such kind of questions?







share|cite|improve this question














Recently, I came across a question:




A train $T_1$ from station $P$ to $Q$, and, the other train $T_2$ from station $Q$ to $P$, start simultaneously. After they meet, the trains reach their destinations after $9$ hours and $16$ hours respectively. The ratio of their speeds is ___.

(i) $2:3$

(ii) $4:3$

(iii) $6:7$

(iv) $9:16$




The only formula I remembered was
$$
textSpeed = fractextDistancetextTime cdotp
$$
I couldn't solve the question. It became more and more complex when I tried using this formula directly. Later I found out that the correct answer is (ii) $4:3$. The only explanation given was $sqrt16:sqrt9$. I can't understand how
$$
sqrtoperatornameTime(T_2) : sqrtoperatornameTime(T_1)
$$
is the right formula to solve such kind of questions?









share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Aug 25 at 8:28









Jendrik Stelzner

7,57221037




7,57221037










asked Aug 24 at 10:17









code_master5

102




102











  • Related to this question.
    – Bill Wallis
    Aug 24 at 10:21






  • 1




    Trying to memorize formulas in order to solve math problems will not get you far. The times the trains needed to reach their destinations were $t+9$ and $t+16$ respectively, $t$ is the time when they met. You know that the distance they traveled was the same, can you figure out the result?
    – tst
    Aug 24 at 10:23











  • To expand on what @tst is saying, if you tried to remember formulas for every question like this, there would be a lot of formulas, and trying to decide which one is appropriate in each case would be a nightmare. It's much better to know a few, really important formulas (like $textspeed = fractextdistancetexttime$) and then derive the formula you need for any other problem using those, use the new formula you just derived, then forget about it.
    – Arthur
    Aug 24 at 10:43











  • @tst I totally agree. That's why I asked the question here to understand how the formula actually works!
    – code_master5
    Aug 25 at 13:01
















  • Related to this question.
    – Bill Wallis
    Aug 24 at 10:21






  • 1




    Trying to memorize formulas in order to solve math problems will not get you far. The times the trains needed to reach their destinations were $t+9$ and $t+16$ respectively, $t$ is the time when they met. You know that the distance they traveled was the same, can you figure out the result?
    – tst
    Aug 24 at 10:23











  • To expand on what @tst is saying, if you tried to remember formulas for every question like this, there would be a lot of formulas, and trying to decide which one is appropriate in each case would be a nightmare. It's much better to know a few, really important formulas (like $textspeed = fractextdistancetexttime$) and then derive the formula you need for any other problem using those, use the new formula you just derived, then forget about it.
    – Arthur
    Aug 24 at 10:43











  • @tst I totally agree. That's why I asked the question here to understand how the formula actually works!
    – code_master5
    Aug 25 at 13:01















Related to this question.
– Bill Wallis
Aug 24 at 10:21




Related to this question.
– Bill Wallis
Aug 24 at 10:21




1




1




Trying to memorize formulas in order to solve math problems will not get you far. The times the trains needed to reach their destinations were $t+9$ and $t+16$ respectively, $t$ is the time when they met. You know that the distance they traveled was the same, can you figure out the result?
– tst
Aug 24 at 10:23





Trying to memorize formulas in order to solve math problems will not get you far. The times the trains needed to reach their destinations were $t+9$ and $t+16$ respectively, $t$ is the time when they met. You know that the distance they traveled was the same, can you figure out the result?
– tst
Aug 24 at 10:23













To expand on what @tst is saying, if you tried to remember formulas for every question like this, there would be a lot of formulas, and trying to decide which one is appropriate in each case would be a nightmare. It's much better to know a few, really important formulas (like $textspeed = fractextdistancetexttime$) and then derive the formula you need for any other problem using those, use the new formula you just derived, then forget about it.
– Arthur
Aug 24 at 10:43





To expand on what @tst is saying, if you tried to remember formulas for every question like this, there would be a lot of formulas, and trying to decide which one is appropriate in each case would be a nightmare. It's much better to know a few, really important formulas (like $textspeed = fractextdistancetexttime$) and then derive the formula you need for any other problem using those, use the new formula you just derived, then forget about it.
– Arthur
Aug 24 at 10:43













@tst I totally agree. That's why I asked the question here to understand how the formula actually works!
– code_master5
Aug 25 at 13:01




@tst I totally agree. That's why I asked the question here to understand how the formula actually works!
– code_master5
Aug 25 at 13:01










1 Answer
1






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oldest

votes

















up vote
3
down vote



accepted










You need to introduce a third point, where they meet: $M$. Then we know the following things:



  1. The time $T_1$ spent on $PM$ is equal to the time $T_2$ spent on $QM$

  2. The time $T_1$ spent on $QM$ is equal to $9$ hours

  3. The time $T_2$ spent on $PM$ is equal to $16$ hours

Also note that $textspeed = fractextdistancetexttime$ becomes $texttime = fractextdistancetextspeed$ with some elementary manipulation. Use this to make equations out of the three above facts, using sensible variables, and note that what we're after is not $textspeed_1$ or $textspeed_2$, but $fractextspeed_1textspeed_2$.




Alternatively, you can game the question, and note that train 1 is clearly faster, and only one option allows that.






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    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes








    up vote
    3
    down vote



    accepted










    You need to introduce a third point, where they meet: $M$. Then we know the following things:



    1. The time $T_1$ spent on $PM$ is equal to the time $T_2$ spent on $QM$

    2. The time $T_1$ spent on $QM$ is equal to $9$ hours

    3. The time $T_2$ spent on $PM$ is equal to $16$ hours

    Also note that $textspeed = fractextdistancetexttime$ becomes $texttime = fractextdistancetextspeed$ with some elementary manipulation. Use this to make equations out of the three above facts, using sensible variables, and note that what we're after is not $textspeed_1$ or $textspeed_2$, but $fractextspeed_1textspeed_2$.




    Alternatively, you can game the question, and note that train 1 is clearly faster, and only one option allows that.






    share|cite|improve this answer


























      up vote
      3
      down vote



      accepted










      You need to introduce a third point, where they meet: $M$. Then we know the following things:



      1. The time $T_1$ spent on $PM$ is equal to the time $T_2$ spent on $QM$

      2. The time $T_1$ spent on $QM$ is equal to $9$ hours

      3. The time $T_2$ spent on $PM$ is equal to $16$ hours

      Also note that $textspeed = fractextdistancetexttime$ becomes $texttime = fractextdistancetextspeed$ with some elementary manipulation. Use this to make equations out of the three above facts, using sensible variables, and note that what we're after is not $textspeed_1$ or $textspeed_2$, but $fractextspeed_1textspeed_2$.




      Alternatively, you can game the question, and note that train 1 is clearly faster, and only one option allows that.






      share|cite|improve this answer
























        up vote
        3
        down vote



        accepted







        up vote
        3
        down vote



        accepted






        You need to introduce a third point, where they meet: $M$. Then we know the following things:



        1. The time $T_1$ spent on $PM$ is equal to the time $T_2$ spent on $QM$

        2. The time $T_1$ spent on $QM$ is equal to $9$ hours

        3. The time $T_2$ spent on $PM$ is equal to $16$ hours

        Also note that $textspeed = fractextdistancetexttime$ becomes $texttime = fractextdistancetextspeed$ with some elementary manipulation. Use this to make equations out of the three above facts, using sensible variables, and note that what we're after is not $textspeed_1$ or $textspeed_2$, but $fractextspeed_1textspeed_2$.




        Alternatively, you can game the question, and note that train 1 is clearly faster, and only one option allows that.






        share|cite|improve this answer














        You need to introduce a third point, where they meet: $M$. Then we know the following things:



        1. The time $T_1$ spent on $PM$ is equal to the time $T_2$ spent on $QM$

        2. The time $T_1$ spent on $QM$ is equal to $9$ hours

        3. The time $T_2$ spent on $PM$ is equal to $16$ hours

        Also note that $textspeed = fractextdistancetexttime$ becomes $texttime = fractextdistancetextspeed$ with some elementary manipulation. Use this to make equations out of the three above facts, using sensible variables, and note that what we're after is not $textspeed_1$ or $textspeed_2$, but $fractextspeed_1textspeed_2$.




        Alternatively, you can game the question, and note that train 1 is clearly faster, and only one option allows that.







        share|cite|improve this answer














        share|cite|improve this answer



        share|cite|improve this answer








        edited Aug 25 at 13:11

























        answered Aug 24 at 10:22









        Arthur

        101k795176




        101k795176



























             

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