Efficiently Solve Difficult Math Problems

  • Thread starter ehrenfest
  • Start date
In summary, the best approach to solving this problem is to calculate the time it takes for the total trip and each segment. This can be done by dividing the distance by the speed. Then, determine whether the time it takes for the last 20 miles is greater than 45 minutes by using long division.
  • #1
ehrenfest
2,020
1

Homework Statement


What is the best way to do this problem? It looked easy but when I the solution just wasn't clicking for me. I tried to calculated the average speed of the last 20 miles explicitly and it took me a really long time and I had to crudely approximate the answer...I am pretty sure there is a simple way to do this.


Homework Equations





The Attempt at a Solution

 

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  • #2
Hint: Figure out the time it takes for the total trip and each segment.
 
  • #3
Doc Al said:
Hint: Figure out the time it takes for the total trip and each segment.

That's pretty much what I did. The first 30 miles take 3/4 hr and the last 20 miles take 13/36 hr. So then I just need to figure out whether 20*36/13 is greater than 45 by long division, right?
 
  • #4
ehrenfest said:
That's pretty much what I did. The first 30 miles take 3/4 hr and the last 20 miles take 13/36 hr. So then I just need to figure out whether 20*36/13 is greater than 45 by long division, right?

That's correct.
 

1. What strategies can I use to efficiently solve difficult math problems?

There are several strategies you can use to efficiently solve difficult math problems. These include breaking the problem down into smaller, manageable steps, identifying patterns and connections within the problem, and working backwards from the solution. Additionally, using visual aids such as diagrams and graphs can also be helpful in finding a solution.

2. How can I improve my problem-solving skills in math?

Improving your problem-solving skills in math requires practice and persistence. It is important to first understand the underlying concepts and principles of math before attempting to solve difficult problems. Regularly practicing with a variety of problems and seeking help from teachers or peers when needed can also greatly improve your problem-solving abilities.

3. How can I stay organized while solving difficult math problems?

Staying organized while solving difficult math problems is crucial for efficiency. One way to do this is to write down all the given information and important equations or formulas before attempting to solve the problem. You can also use a step-by-step approach, writing down each step as you go, to ensure you don't miss any important steps.

4. Are there any common mistakes to avoid when solving difficult math problems?

Yes, there are a few common mistakes to avoid when solving difficult math problems. These include rushing through the problem without fully understanding it, making careless arithmetic errors, and using incorrect formulas or equations. It is important to take your time, double-check your work, and always go back to the given information to ensure you are on the right track.

5. How can I overcome my fear of solving difficult math problems?

Many people experience anxiety or fear when faced with difficult math problems. To overcome this fear, it is important to have a positive mindset and believe in your own abilities. Remind yourself that it is okay to make mistakes and that solving problems is a learning process. Seek help from teachers or peers if needed, and practice regularly to build your confidence and skills in solving difficult math problems.

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