Why is my solution to this particular word problem incorrect?
$begingroup$
I have a situation with 3 cars: A, B, and C. Cars B and C start at the same spot, while car A is already 15km ahead:
The velocities of the cars are:
$V_A = 50km/h$
$V_B = 40km/h$
$V_C = 60km/h$
The question is: is it possible that car C can be located exactly between car B and car A? The final answer dictates that the situation is not possible, but the equation I made suggests that it is, so I assume I made a mistake somewhere, but I can't seem to find where.
Here is how I did it:
Assume $t$ is the number of hours it took for the requested situation to occur:
It is obvious now that car C is just an average of the distances traveled by car A & B. If a solution exists, the following equation must be true:
$$frac{(50t + 15) + 40t}{2} = 60t$$
When we try to solve for $t$, we get that:
$$90t + 15 = 120t rightarrow 30t = 15 rightarrow t = 1/2 text{ hours}$$
If a solution exists, then the situation must occur -- this contrasts the final answer. Where is my mistake?
word-problem
edited Dec 11 '18 at 16:17
Ethan Bolker
42.5k549113
asked Dec 11 '18 at 16:10
daedsidogdaedsidog
29017
$endgroup$
add a comment |
$begingroup$
I have a situation with 3 cars: A, B, and C. Cars B and C start at the same spot, while car A is already 15km ahead:
The velocities of the cars are:
$V_A = 50km/h$
$V_B = 40km/h$
$V_C = 60km/h$
The question is: is it possible that car C can be located exactly between car B and car A? The final answer dictates that the situation is not possible, but the equation I made suggests that it is, so I assume I made a mistake somewhere, but I can't seem to find where.
Here is how I did it:
Assume $t$ is the number of hours it took for the requested situation to occur:
It is obvious now that car C is just an average of the distances traveled by car A & B. If a solution exists, the following equation must be true:
$$frac{(50t + 15) + 40t}{2} = 60t$$
When we try to solve for $t$, we get that:
$$90t + 15 = 120t rightarrow 30t = 15 rightarrow t = 1/2 text{ hours}$$
If a solution exists, then the situation must occur -- this contrasts the final answer. Where is my mistake?
word-problem
edited Dec 11 '18 at 16:17
Ethan Bolker
42.5k549113
asked Dec 11 '18 at 16:10
daedsidogdaedsidog
29017
$endgroup$
$begingroup$
Your reasoning looks good and your answer checks: the cars are at positions $40$, $20$ and $30$. Are you sure you stated the problem correctly and quoted the "answer" correctly?
$endgroup$
– Ethan Bolker
Dec 11 '18 at 16:17
2
$begingroup$
I have triple checked and everything is in order. My only conclusion is that the final answer (which is not expanded upon) must be incorrect.
$endgroup$
– daedsidog
Dec 11 '18 at 16:20
add a comment |
$begingroup$
I have a situation with 3 cars: A, B, and C. Cars B and C start at the same spot, while car A is already 15km ahead:
The velocities of the cars are:
$V_A = 50km/h$
$V_B = 40km/h$
$V_C = 60km/h$
The question is: is it possible that car C can be located exactly between car B and car A? The final answer dictates that the situation is not possible, but the equation I made suggests that it is, so I assume I made a mistake somewhere, but I can't seem to find where.
Here is how I did it:
Assume $t$ is the number of hours it took for the requested situation to occur:
It is obvious now that car C is just an average of the distances traveled by car A & B. If a solution exists, the following equation must be true:
$$frac{(50t + 15) + 40t}{2} = 60t$$
When we try to solve for $t$, we get that:
$$90t + 15 = 120t rightarrow 30t = 15 rightarrow t = 1/2 text{ hours}$$
If a solution exists, then the situation must occur -- this contrasts the final answer. Where is my mistake?
word-problem
edited Dec 11 '18 at 16:17
Ethan Bolker
42.5k549113
asked Dec 11 '18 at 16:10
daedsidogdaedsidog
29017
$endgroup$
I have a situation with 3 cars: A, B, and C. Cars B and C start at the same spot, while car A is already 15km ahead:
The velocities of the cars are:
$V_A = 50km/h$
$V_B = 40km/h$
$V_C = 60km/h$
The question is: is it possible that car C can be located exactly between car B and car A? The final answer dictates that the situation is not possible, but the equation I made suggests that it is, so I assume I made a mistake somewhere, but I can't seem to find where.
Here is how I did it:
Assume $t$ is the number of hours it took for the requested situation to occur:
It is obvious now that car C is just an average of the distances traveled by car A & B. If a solution exists, the following equation must be true:
$$frac{(50t + 15) + 40t}{2} = 60t$$
When we try to solve for $t$, we get that:
$$90t + 15 = 120t rightarrow 30t = 15 rightarrow t = 1/2 text{ hours}$$
If a solution exists, then the situation must occur -- this contrasts the final answer. Where is my mistake?
word-problem
word-problem
edited Dec 11 '18 at 16:17
Ethan Bolker
42.5k549113
asked Dec 11 '18 at 16:10
daedsidogdaedsidog
29017
edited Dec 11 '18 at 16:17
Ethan Bolker
42.5k549113
asked Dec 11 '18 at 16:10
daedsidogdaedsidog
29017
edited Dec 11 '18 at 16:17
Ethan Bolker
42.5k549113
edited Dec 11 '18 at 16:17
Ethan Bolker
42.5k549113
edited Dec 11 '18 at 16:17
Ethan Bolker
42.5k549113
42.5k549113
asked Dec 11 '18 at 16:10
daedsidogdaedsidog
29017
asked Dec 11 '18 at 16:10
daedsidogdaedsidog
29017
asked Dec 11 '18 at 16:10
daedsidogdaedsidog
29017
29017
$begingroup$
Your reasoning looks good and your answer checks: the cars are at positions $40$, $20$ and $30$. Are you sure you stated the problem correctly and quoted the "answer" correctly?
$endgroup$
– Ethan Bolker
Dec 11 '18 at 16:17
2
$begingroup$
I have triple checked and everything is in order. My only conclusion is that the final answer (which is not expanded upon) must be incorrect.
$endgroup$
– daedsidog
Dec 11 '18 at 16:20
add a comment |
$begingroup$
Your reasoning looks good and your answer checks: the cars are at positions $40$, $20$ and $30$. Are you sure you stated the problem correctly and quoted the "answer" correctly?
$endgroup$
– Ethan Bolker
Dec 11 '18 at 16:17
2
$begingroup$
I have triple checked and everything is in order. My only conclusion is that the final answer (which is not expanded upon) must be incorrect.
$endgroup$
– daedsidog
Dec 11 '18 at 16:20
$begingroup$
Your reasoning looks good and your answer checks: the cars are at positions $40$, $20$ and $30$. Are you sure you stated the problem correctly and quoted the "answer" correctly?
$endgroup$
– Ethan Bolker
Dec 11 '18 at 16:17
$begingroup$
Your reasoning looks good and your answer checks: the cars are at positions $40$, $20$ and $30$. Are you sure you stated the problem correctly and quoted the "answer" correctly?
$endgroup$
– Ethan Bolker
Dec 11 '18 at 16:17
2
2
$begingroup$
I have triple checked and everything is in order. My only conclusion is that the final answer (which is not expanded upon) must be incorrect.
$endgroup$
– daedsidog
Dec 11 '18 at 16:20
$begingroup$
I have triple checked and everything is in order. My only conclusion is that the final answer (which is not expanded upon) must be incorrect.
$endgroup$
– daedsidog
Dec 11 '18 at 16:20
add a comment |
1 Answer
1
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$begingroup$
You are correct. After $frac 12$ hour, $A$ is at $40$ km, $B$ is at $20$ km, $C$ is at $30$ km and $C$ is indeed halfway in between.
answered Dec 11 '18 at 16:18
Ross MillikanRoss Millikan
295k23198371
$endgroup$
add a comment |
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$begingroup$
You are correct. After $frac 12$ hour, $A$ is at $40$ km, $B$ is at $20$ km, $C$ is at $30$ km and $C$ is indeed halfway in between.
answered Dec 11 '18 at 16:18
Ross MillikanRoss Millikan
295k23198371
$endgroup$
add a comment |
$begingroup$
You are correct. After $frac 12$ hour, $A$ is at $40$ km, $B$ is at $20$ km, $C$ is at $30$ km and $C$ is indeed halfway in between.
answered Dec 11 '18 at 16:18
Ross MillikanRoss Millikan
295k23198371
$endgroup$
add a comment |
$begingroup$
You are correct. After $frac 12$ hour, $A$ is at $40$ km, $B$ is at $20$ km, $C$ is at $30$ km and $C$ is indeed halfway in between.
answered Dec 11 '18 at 16:18
Ross MillikanRoss Millikan
295k23198371
$endgroup$
You are correct. After $frac 12$ hour, $A$ is at $40$ km, $B$ is at $20$ km, $C$ is at $30$ km and $C$ is indeed halfway in between.
answered Dec 11 '18 at 16:18
Ross MillikanRoss Millikan
295k23198371
answered Dec 11 '18 at 16:18
Ross MillikanRoss Millikan
295k23198371
answered Dec 11 '18 at 16:18
Ross MillikanRoss Millikan
295k23198371
answered Dec 11 '18 at 16:18
Ross MillikanRoss Millikan
295k23198371
295k23198371
add a comment |
add a comment |
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$begingroup$
Your reasoning looks good and your answer checks: the cars are at positions $40$, $20$ and $30$. Are you sure you stated the problem correctly and quoted the "answer" correctly?
$endgroup$
– Ethan Bolker
Dec 11 '18 at 16:17
2
$begingroup$
I have triple checked and everything is in order. My only conclusion is that the final answer (which is not expanded upon) must be incorrect.
$endgroup$
– daedsidog
Dec 11 '18 at 16:20