What Was Your Original Speed on the Freeway?

In summary, the conversation discusses a problem involving a car's speed on a crowded freeway. By using the equation D = VT, the original speed is found to be 0.022 mph. However, there is a mistake in the calculation and the correct answer is still unknown. The conversation also suggests using another relation between the original speed and time to find the solution.
  • #1
zeromodz
246
0

Homework Statement


Driving along a crowded freeway, you notice that it takes a time t to go from one mile marker to the next. When you increase your speed by 7.0 mi/h, the time to go one mile decreases by 12 s. What was your original speed?


Homework Equations


D = VT

The Attempt at a Solution



D = VT
1 = (Vi+7)(T-0.2)
Vi = 1/(T-0.2) - 7

I have 2 unknowns and I don't know how to solve?
 
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  • #2
zeromodz said:
D = VT
1 = (Vi+7)(T-0.2)
Vi = 1/(T-0.2) - 7

I have 2 unknowns and I don't know how to solve?

You are almost done! You know the value of D, and by eliminating T from the first two equations you shold get the right answer.
 
  • #3
N-Gin said:
You are almost done! You know the value of D, and by eliminating T from the first two equations you shold get the right answer.

I can't solve it. I ended up with

V = 1/(1/V-0.2) - 7
 
  • #4
Originally, it took T hours to travel 1 mile with Vi speed.

ehild
 
  • #5
Can someone please tell me how to solve this instead of beating around the bush?
 
  • #6
The distance [itex]D = 1 \, \mathrm{mi}[/itex]. Also, [itex]12 \, \mathrm{s} = 1/5 \, \mathrm{min} = 1/300 \, \mathrm{h}[/itex].
 
  • #7
Hint: There's another relation between [itex]v_{i}[/itex] and [itex]t[/itex] that you have not taken into account.
 
  • #8
Dickfore said:
Hint: There's another relation between [itex]v_{i}[/itex] and [itex]t[/itex] that you have not taken into account.

I have tried that, I just cannot find the answer.
 
  • #9
zeromodz said:
I have tried that, I just cannot find the answer.

You tried solving both equations for V_i and you couldn't find the answer? Did you get a quadratic equation?
 
  • #10
zeromodz said:
I have tried that, I just cannot find the answer.

zeromodz said:
I can't solve it. I ended up with

V = 1/(1/V-0.2) - 7

This is an equation with one unknown that can be further simplified. However, it is wrong because you had not converted 12 s into hours correctly.
 
  • #11
Dickfore said:
This is an equation with one unknown that can be further simplified. However, it is wrong because you had not converted 12 s into hours correctly.

Sorry, it would be

V = 1/(1/V-0.00333) - 7

I still don't know how to solve for V
 
  • #12
Get rid of the double fractions first and then multiply everything with the common denominator to get rid of fractions.
 
  • #13
Dickfore said:
Get rid of the double fractions first and then multiply everything with the common denominator to get rid of fractions.

V = 1/(1/V-0.00333) - 7
V = -V/0.003333 - 7
V + 7 = -V/0.0033333
0.003333V + 0.0233333 = -V
0.003333V + V = 0.023333
V(0.00333 + 1) = 0.023333
V = 0.023333 / (0.00333 + 1)
V = 0.022 mph?
 
  • #14
zeromodz said:
V = 1/(1/V-0.00333) - 7
V = -V/0.003333 - 7

This is incorrect.
 
  • #15
Dickfore said:
This is incorrect.
How is it incorrect? If you take

1 / 2 / 3 = 3 / 2
 
  • #16
But, this is not what you have. There is a "-" sign in there. Also, if you take:

zeromodz said:
How is it incorrect? If you take

1 / 2 / 3 = 3 / 2

as it is written, it might mean:

(1/2)/3 = 1/6 or 1/(2/3) = 3/2

so you have to be careful with your notation. I suggest learning LaTeX:

[tex]
\frac{1}{\frac{2}{3}} = \frac{3}{2}
[/tex]
 

Related to What Was Your Original Speed on the Freeway?

1. What steps should I take to start solving the problem?

To begin solving a problem, it's helpful to break it down into smaller, more manageable parts. Start by identifying the main question or issue that needs to be addressed. Then, gather all the relevant information and data related to the problem. Next, brainstorm potential solutions or approaches. And finally, evaluate each solution and determine the best course of action.

2. How can I stay motivated and focused while trying to solve a difficult problem?

One way to stay motivated is to remind yourself of the importance and potential impact of solving the problem. Additionally, taking breaks and engaging in activities that help clear your mind can prevent burnout and keep you focused. Collaborating with others or seeking advice from experts can also provide a fresh perspective and help generate new ideas.

3. What if I don't have enough information or knowledge to solve the problem?

If you feel like you don't have enough information or knowledge to solve a problem, take a step back and reassess. Identify any knowledge gaps and do some research to fill them in. Seek out resources, such as books, articles, or experts, that can provide additional information and insights. Don't be afraid to ask for help or advice from others who may have more expertise in the subject matter.

4. How do I know if I've found the right solution?

The right solution will address the main question or issue and be supported by evidence and data. It should also align with any constraints or limitations and be feasible to implement. It's important to carefully evaluate and test any potential solution before fully implementing it. Seeking feedback from others can also help determine if the solution is sound and effective.

5. How can I prevent similar problems from arising in the future?

To prevent similar problems from occurring in the future, it's important to reflect on the root cause of the problem and identify any patterns or underlying issues. Consider implementing preventative measures, such as establishing protocols or procedures, to address potential issues before they arise. Additionally, learning from mistakes and continually seeking to improve can help prevent future problems.

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