Ratio of Speeds of Trains
Clash Royale CLAN TAG#URR8PPP
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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?
ratio
add a comment |Â
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?
ratio
Related to this question.
â 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?
â 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.
â 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!
â code_master5
Aug 25 at 13:01
add a comment |Â
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?
ratio
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?
ratio
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.
â 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?
â 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.
â 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!
â code_master5
Aug 25 at 13:01
add a comment |Â
Related to this question.
â 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?
â 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.
â 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!
â code_master5
Aug 25 at 13:01
Related to this question.
â Bill Wallis
Aug 24 at 10:21
Related to this question.
â 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?
â 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?
â 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.
â 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.
â 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!
â 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!
â code_master5
Aug 25 at 13:01
add a comment |Â
1 Answer
1
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:
- The time $T_1$ spent on $PM$ is equal to the time $T_2$ spent on $QM$
- The time $T_1$ spent on $QM$ is equal to $9$ hours
- 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.
add a comment |Â
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:
- The time $T_1$ spent on $PM$ is equal to the time $T_2$ spent on $QM$
- The time $T_1$ spent on $QM$ is equal to $9$ hours
- 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.
add a comment |Â
up vote
3
down vote
accepted
You need to introduce a third point, where they meet: $M$. Then we know the following things:
- The time $T_1$ spent on $PM$ is equal to the time $T_2$ spent on $QM$
- The time $T_1$ spent on $QM$ is equal to $9$ hours
- 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.
add a comment |Â
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:
- The time $T_1$ spent on $PM$ is equal to the time $T_2$ spent on $QM$
- The time $T_1$ spent on $QM$ is equal to $9$ hours
- 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.
You need to introduce a third point, where they meet: $M$. Then we know the following things:
- The time $T_1$ spent on $PM$ is equal to the time $T_2$ spent on $QM$
- The time $T_1$ spent on $QM$ is equal to $9$ hours
- 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.
edited Aug 25 at 13:11
answered Aug 24 at 10:22
Arthur
101k795176
101k795176
add a comment |Â
add a comment |Â
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Related to this question.
â 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?
â 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.
â 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!
â code_master5
Aug 25 at 13:01