A Car Traveling At A Constant Speed Covers 30 Km In 15 Minutes. How Far Will It Travel In 2 Hours And 12 Minutes If It Continues At The Same Constant Speed?

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Understanding the Problem

To solve this problem, we need to understand the relationship between distance, speed, and time. The formula to calculate distance is given by:

Distance = Speed × Time

We are given that the car covers a distance of 30 km in 15 minutes. We need to find out how far it will travel in 2 hours and 12 minutes.

Converting Time to a Common Unit

Before we can solve the problem, we need to convert the time from minutes to hours. There are 60 minutes in an hour, so:

  • 15 minutes = 15/60 = 0.25 hours
  • 2 hours and 12 minutes = 2 + 12/60 = 2.2 hours

Finding the Speed of the Car

We know that the car covers a distance of 30 km in 0.25 hours. We can use this information to find the speed of the car:

Speed = Distance / Time = 30 km / 0.25 hours = 120 km/h

Calculating the Distance Traveled in 2 Hours and 12 Minutes

Now that we know the speed of the car, we can use it to find the distance traveled in 2 hours and 12 minutes:

Distance = Speed × Time = 120 km/h × 2.2 hours = 264 km

Conclusion

Therefore, if the car continues to travel at the same constant speed, it will cover a distance of 264 km in 2 hours and 12 minutes.

Real-World Applications

This problem has many real-world applications, such as:

  • Traffic flow: Understanding the relationship between speed and distance is crucial in traffic flow management. It helps engineers design roads and intersections that can handle a large volume of traffic.
  • Transportation planning: Knowing the speed of a vehicle and the distance it travels is essential in transportation planning. It helps planners design routes and schedules that are efficient and safe.
  • Logistics: Understanding the speed and distance of a vehicle is critical in logistics. It helps companies plan and manage their supply chains, ensuring that goods are delivered on time and in good condition.

Tips and Tricks

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

  • Use the correct units: Make sure to use the correct units of measurement, such as kilometers per hour (km/h) or miles per hour (mph).
  • Convert time to a common unit: Convert time from minutes to hours to make it easier to calculate the distance.
  • Use the formula: Use the formula Distance = Speed × Time to calculate the distance traveled.
  • Check your units: Double-check your units to ensure that they are consistent.

Practice Problems

Here are some practice problems to help you practice solving problems like this:

  • A car travels at a speed of 80 km/h. How far will it travel in 3 hours?
  • A bicycle travels at a speed of 20 km/h. How far will it travel in 2 hours?
  • A train travels at a speed of 60 km/h. How far will it travel in 4 hours?

Conclusion

In conclusion, understanding the relationship between speed and distance is crucial in many real-world applications. By using the formula Distance = Speed × Time, we can calculate the distance traveled by a vehicle. Remember to use the correct units, convert time to a common unit, and check your units to ensure that they are consistent. With practice, you will become proficient in solving problems like this.

Understanding the Problem

To solve this problem, we need to understand the relationship between distance, speed, and time. The formula to calculate distance is given by:

Distance = Speed × Time

We are given that the car covers a distance of 30 km in 15 minutes. We need to find out how far it will travel in 2 hours and 12 minutes.

Converting Time to a Common Unit

Before we can solve the problem, we need to convert the time from minutes to hours. There are 60 minutes in an hour, so:

  • 15 minutes = 15/60 = 0.25 hours
  • 2 hours and 12 minutes = 2 + 12/60 = 2.2 hours

Finding the Speed of the Car

We know that the car covers a distance of 30 km in 0.25 hours. We can use this information to find the speed of the car:

Speed = Distance / Time = 30 km / 0.25 hours = 120 km/h

Calculating the Distance Traveled in 2 Hours and 12 Minutes

Now that we know the speed of the car, we can use it to find the distance traveled in 2 hours and 12 minutes:

Distance = Speed × Time = 120 km/h × 2.2 hours = 264 km

Conclusion

Therefore, if the car continues to travel at the same constant speed, it will cover a distance of 264 km in 2 hours and 12 minutes.

Real-World Applications

This problem has many real-world applications, such as:

  • Traffic flow: Understanding the relationship between speed and distance is crucial in traffic flow management. It helps engineers design roads and intersections that can handle a large volume of traffic.
  • Transportation planning: Knowing the speed of a vehicle and the distance it travels is essential in transportation planning. It helps planners design routes and schedules that are efficient and safe.
  • Logistics: Understanding the speed and distance of a vehicle is critical in logistics. It helps companies plan and manage their supply chains, ensuring that goods are delivered on time and in good condition.

Tips and Tricks

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

  • Use the correct units: Make sure to use the correct units of measurement, such as kilometers per hour (km/h) or miles per hour (mph).
  • Convert time to a common unit: Convert time from minutes to hours to make it easier to calculate the distance.
  • Use the formula: Use the formula Distance = Speed × Time to calculate the distance traveled.
  • Check your units: Double-check your units to ensure that they are consistent.

Practice Problems

Here are some practice problems to help you practice solving problems like this:

  • A car travels at a speed of 80 km/h. How far will it travel in 3 hours?
  • A bicycle travels at a speed of 20 km/h. How far will it travel in 2 hours?
  • A train travels at a speed of 60 km/h. How far will it travel in 4 hours?

Q&A

Q: What is the formula to calculate distance?

A: The formula to calculate distance is given by: Distance = Speed × Time

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

A: To convert time from minutes to hours, divide the number of minutes by 60.

Q: What is the speed of the car in the problem?

A: The speed of the car is 120 km/h.

Q: How far will the car travel in 2 hours and 12 minutes?

A: The car will travel a distance of 264 km in 2 hours and 12 minutes.

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

A: Some real-world applications of this problem include traffic flow management, transportation planning, and logistics.

Q: How do I check my units to ensure they are consistent?

A: To check your units, make sure that the units of speed and time are consistent. For example, if the speed is given in kilometers per hour (km/h), make sure that the time is given in hours.

Q: Can I use this formula to calculate the distance traveled by a vehicle that is accelerating or decelerating?

A: No, this formula is only applicable to vehicles that are traveling at a constant speed. If the vehicle is accelerating or decelerating, you will need to use a different formula to calculate the distance traveled.

Q: How do I practice solving problems like this?

A: You can practice solving problems like this by using the formula Distance = Speed × Time and converting time from minutes to hours. You can also try solving practice problems, such as the ones listed above.

Conclusion

In conclusion, understanding the relationship between speed and distance is crucial in many real-world applications. By using the formula Distance = Speed × Time, we can calculate the distance traveled by a vehicle. Remember to use the correct units, convert time to a common unit, and check your units to ensure that they are consistent. With practice, you will become proficient in solving problems like this.