A Car Travels 180 Km In 2 Hours On A Straight Road. How Far Can The Car Travel In 210 Minutes At The Same Speed?

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Understanding the Problem

To solve this problem, we need to understand the relationship between distance, speed, and time. The car travels 180 km in 2 hours, and we want to find out how far it can travel in 210 minutes at the same speed. We will use the formula: distance = speed × time.

Converting Time from Hours to Minutes

First, let's convert the time from hours to minutes. We know that 1 hour is equal to 60 minutes. So, 2 hours is equal to 2 × 60 = 120 minutes. Now, we have the time in minutes: 120 minutes.

Finding the Speed of the Car

To find the speed of the car, we will use the formula: speed = distance ÷ time. We know that the car travels 180 km in 120 minutes. So, the speed of the car is: 180 km ÷ 120 minutes = 1.5 km/minute.

Finding the Distance Traveled in 210 Minutes

Now that we know the speed of the car, we can find the distance traveled in 210 minutes. We will use the formula: distance = speed × time. We know that the speed of the car is 1.5 km/minute, and the time is 210 minutes. So, the distance traveled is: 1.5 km/minute × 210 minutes = 315 km.

Conclusion

In conclusion, the car can travel 315 km in 210 minutes at the same speed.

Real-World Applications

This problem has real-world applications in various fields such as:

  • Transportation: Understanding the relationship between distance, speed, and time is crucial in transportation planning, traffic management, and route optimization.
  • Logistics: Companies need to calculate the distance and time required to transport goods from one location to another, which is essential for efficient logistics and supply chain management.
  • Travel: Travelers need to calculate the distance and time required to travel from one location to another, which is essential for planning trips and making informed decisions.

Tips and Tricks

Here are some tips and tricks to help you solve this problem:

  • Use the correct units: Make sure to use the correct units of measurement, such as kilometers, minutes, and hours.
  • Convert time: Convert time from hours to minutes or vice versa to ensure accuracy.
  • Use the formula: Use the formula: distance = speed × time to find the distance traveled.
  • Check your units: Check your units to ensure that they are consistent and accurate.

Common Mistakes

Here are some common mistakes to avoid when solving this problem:

  • Incorrect units: Using incorrect units of measurement, such as kilometers per hour instead of kilometers per minute.
  • Incorrect conversion: Converting time incorrectly, such as converting 2 hours to 120 seconds instead of 120 minutes.
  • Incorrect formula: Using the incorrect formula, such as distance = speed ÷ time instead of distance = speed × time.
  • Lack of unit consistency: Failing to check for unit consistency, such as using kilometers per minute and hours as units of time.

Additional Resources

For more information on this topic, you can refer to the following resources:

  • Math textbooks: Math textbooks that cover algebra and geometry, such as "Algebra and Trigonometry" by Michael Sullivan.
  • Online resources: Online resources such as Khan Academy, Mathway, and Wolfram Alpha.
  • Math websites: Math websites such as Math Open Reference, Math Is Fun, and Purplemath.

Conclusion

In conclusion, the car can travel 315 km in 210 minutes at the same speed. This problem has real-world applications in various fields such as transportation, logistics, and travel. By following the tips and tricks and avoiding common mistakes, you can solve this problem accurately and efficiently.

Q: What is the speed of the car?

A: To find the speed of the car, we need to use the formula: speed = distance ÷ time. We know that the car travels 180 km in 120 minutes. So, the speed of the car is: 180 km ÷ 120 minutes = 1.5 km/minute.

Q: How do I convert time from hours to minutes?

A: To convert time from hours to minutes, we need to multiply the number of hours by 60. For example, 2 hours is equal to 2 × 60 = 120 minutes.

Q: What is the distance traveled in 210 minutes?

A: Now that we know the speed of the car, we can find the distance traveled in 210 minutes. We will use the formula: distance = speed × time. We know that the speed of the car is 1.5 km/minute, and the time is 210 minutes. So, the distance traveled is: 1.5 km/minute × 210 minutes = 315 km.

Q: What are some real-world applications of this problem?

A: This problem has real-world applications in various fields such as:

  • Transportation: Understanding the relationship between distance, speed, and time is crucial in transportation planning, traffic management, and route optimization.
  • Logistics: Companies need to calculate the distance and time required to transport goods from one location to another, which is essential for efficient logistics and supply chain management.
  • Travel: Travelers need to calculate the distance and time required to travel from one location to another, which is essential for planning trips and making informed decisions.

Q: What are some tips and tricks to help me solve this problem?

A: Here are some tips and tricks to help you solve this problem:

  • Use the correct units: Make sure to use the correct units of measurement, such as kilometers, minutes, and hours.
  • Convert time: Convert time from hours to minutes or vice versa to ensure accuracy.
  • Use the formula: Use the formula: distance = speed × time to find the distance traveled.
  • Check your units: Check your units to ensure that they are consistent and accurate.

Q: What are some common mistakes to avoid when solving this problem?

A: Here are some common mistakes to avoid when solving this problem:

  • Incorrect units: Using incorrect units of measurement, such as kilometers per hour instead of kilometers per minute.
  • Incorrect conversion: Converting time incorrectly, such as converting 2 hours to 120 seconds instead of 120 minutes.
  • Incorrect formula: Using the incorrect formula, such as distance = speed ÷ time instead of distance = speed × time.
  • Lack of unit consistency: Failing to check for unit consistency, such as using kilometers per minute and hours as units of time.

Q: Where can I find more information on this topic?

A: For more information on this topic, you can refer to the following resources:

  • Math textbooks: Math textbooks that cover algebra and geometry, such as "Algebra and Trigonometry" by Michael Sullivan.
  • Online resources: Online resources such as Khan Academy, Mathway, and Wolfram Alpha.
  • Math websites: Math websites such as Math Open Reference, Math Is Fun, and Purplemath.

Q: How can I apply this problem to real-world situations?

A: This problem can be applied to real-world situations in various fields such as transportation, logistics, and travel. For example, you can use this problem to calculate the distance and time required to travel from one location to another, or to plan a trip and make informed decisions.

Q: What are some other problems that involve distance, speed, and time?

A: Some other problems that involve distance, speed, and time include:

  • A car travels 240 km in 4 hours. How far can the car travel in 6 hours at the same speed?
  • A train travels 360 km in 6 hours. How far can the train travel in 9 hours at the same speed?
  • A plane travels 480 km in 8 hours. How far can the plane travel in 12 hours at the same speed?

Q: How can I practice solving problems like this?

A: You can practice solving problems like this by:

  • Using online resources: Using online resources such as Khan Academy, Mathway, and Wolfram Alpha to practice solving problems.
  • Working with a tutor: Working with a tutor to practice solving problems and get feedback.
  • Solving problems on your own: Solving problems on your own and checking your answers with a calculator or online resource.

Q: What are some other math concepts that involve distance, speed, and time?

A: Some other math concepts that involve distance, speed, and time include:

  • Motion: Motion is the change in position of an object over time.
  • Velocity: Velocity is the rate of change of position of an object with respect to time.
  • Acceleration: Acceleration is the rate of change of velocity of an object with respect to time.

Q: How can I apply these math concepts to real-world situations?

A: These math concepts can be applied to real-world situations in various fields such as transportation, logistics, and travel. For example, you can use these concepts to calculate the distance and time required to travel from one location to another, or to plan a trip and make informed decisions.