Two Cars Are 30 Km Apart And Traveling Towards Each Other. Car A Is Traveling At 60 Km/hr 60 \text{ Km/hr} 60 Km/hr While Car B Is Traveling At 90 Km/hr 90 \text{ Km/hr} 90 Km/hr . After How Many Minutes Will They Pass Each Other?Let X X X Be The Number Of

Introduction

In the world of mathematics, problems often arise from everyday situations, and the scenario of two cars meeting on the highway is a classic example. In this article, we will delve into the mathematical analysis of two cars traveling towards each other and determine the time it takes for them to pass each other. We will use the concept of relative motion and the formula for distance to solve this problem.

The Problem

Two cars, Car A and Car B, are initially 30 km apart. Car A is traveling at a speed of $60 \text{ km/hr}$, while Car B is traveling at a speed of $90 \text{ km/hr}$. We need to find the time it takes for the two cars to meet each other.

Relative Motion

When two objects are moving towards each other, we can use the concept of relative motion to analyze their motion. The relative speed of the two objects is the sum of their individual speeds. In this case, the relative speed of Car A and Car B is $60 \text{ km/hr} + 90 \text{ km/hr} = 150 \text{ km/hr}$.

Distance Formula

The distance formula is given by:

$$d = rt$$

where $d$ is the distance traveled, $r$ is the rate (or speed), and $t$ is the time taken. We can use this formula to find the time it takes for the two cars to meet each other.

Solving the Problem

Let $x$ be the number of hours it takes for the two cars to meet each other. We can set up the equation:

$$30 = 150x$$

To solve for $x$, we can divide both sides of the equation by 150:

$$x = \frac{30}{150}$$

$$x = \frac{1}{5}$$

Therefore, it takes $\frac{1}{5}$ hours for the two cars to meet each other.

Converting to Minutes

To convert the time from hours to minutes, we can multiply the number of hours by 60:

$$\frac{1}{5} \times 60 = 12$$

Therefore, it takes 12 minutes for the two cars to meet each other.

Conclusion

In this article, we analyzed the problem of two cars meeting on the highway using the concept of relative motion and the distance formula. We found that it takes $\frac{1}{5}$ hours, or 12 minutes, for the two cars to meet each other. This problem is a classic example of how mathematics can be used to solve real-world problems.

Real-World Applications

The concept of relative motion and the distance formula have many real-world applications. For example, in physics, we can use these concepts to analyze the motion of objects in different situations. In engineering, we can use these concepts to design and optimize systems that involve motion.

Final Thoughts

In conclusion, the problem of two cars meeting on the highway is a classic example of how mathematics can be used to solve real-world problems. By using the concept of relative motion and the distance formula, we can analyze the motion of objects and determine the time it takes for them to meet each other. This problem has many real-world applications and is an important concept in mathematics and physics.

Additional Resources

For those who want to learn more about relative motion and the distance formula, here are some additional resources:

• Khan Academy: Relative Motion
• MIT OpenCourseWare: Physics 8.01: Relative Motion
• Wolfram MathWorld: Distance Formula

References

• Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of Physics. John Wiley & Sons.
• Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers. Cengage Learning.

Appendix

Here is the solution to the problem in a step-by-step format:

1. Define the problem: Two cars, Car A and Car B, are initially 30 km apart. Car A is traveling at a speed of $60 \text{ km/hr}$, while Car B is traveling at a speed of $90 \text{ km/hr}$.
2. Use the concept of relative motion to analyze the motion of the two cars. The relative speed of the two cars is $60 \text{ km/hr} + 90 \text{ km/hr} = 150 \text{ km/hr}$.
3. Use the distance formula to find the time it takes for the two cars to meet each other: $d = rt$.
4. Set up the equation: $30 = 150x$.
5. Solve for $x$: $x = \frac{30}{150} = \frac{1}{5}$.
6. Convert the time from hours to minutes: $\frac{1}{5} \times 60 = 12$.

Introduction

In our previous article, we analyzed the problem of two cars meeting on the highway using the concept of relative motion and the distance formula. We found that it takes $\frac{1}{5}$ hours, or 12 minutes, for the two cars to meet each other. In this article, we will answer some frequently asked questions related to this problem.

Q&A

Q: What is the relative speed of the two cars?

A: The relative speed of the two cars is the sum of their individual speeds. In this case, the relative speed of Car A and Car B is $60 \text{ km/hr} + 90 \text{ km/hr} = 150 \text{ km/hr}$.

Q: How do we calculate the time it takes for the two cars to meet each other?

A: We can use the distance formula to calculate the time it takes for the two cars to meet each other. The distance formula is given by:

$$d = rt$$

where $d$ is the distance traveled, $r$ is the rate (or speed), and $t$ is the time taken.

Q: What is the distance between the two cars?

A: The distance between the two cars is 30 km.

Q: How do we convert the time from hours to minutes?

A: We can convert the time from hours to minutes by multiplying the number of hours by 60.

Q: What is the time it takes for the two cars to meet each other?

A: The time it takes for the two cars to meet each other is $\frac{1}{5}$ hours, or 12 minutes.

Q: What if the two cars are traveling at different speeds, but in the same direction?

A: If the two cars are traveling at different speeds, but in the same direction, we can use the concept of relative motion to analyze their motion. The relative speed of the two cars is the difference between their individual speeds.

Q: What if the two cars are traveling at the same speed, but in opposite directions?

A: If the two cars are traveling at the same speed, but in opposite directions, we can use the concept of relative motion to analyze their motion. The relative speed of the two cars is the sum of their individual speeds.

Q: Can we use the concept of relative motion to analyze the motion of more than two objects?

A: Yes, we can use the concept of relative motion to analyze the motion of more than two objects. We can consider the motion of each object relative to the others, and then use the concept of relative motion to analyze their motion.

Q: What are some real-world applications of the concept of relative motion?

A: The concept of relative motion has many real-world applications, including:

• Physics: We can use the concept of relative motion to analyze the motion of objects in different situations.
• Engineering: We can use the concept of relative motion to design and optimize systems that involve motion.
• Transportation: We can use the concept of relative motion to analyze the motion of vehicles on the road.

Conclusion

In this article, we answered some frequently asked questions related to the problem of two cars meeting on the highway. We used the concept of relative motion and the distance formula to analyze the motion of the two cars and determine the time it takes for them to meet each other. We also discussed some real-world applications of the concept of relative motion.

Additional Resources

For those who want to learn more about relative motion and the distance formula, here are some additional resources:

• Khan Academy: Relative Motion
• MIT OpenCourseWare: Physics 8.01: Relative Motion
• Wolfram MathWorld: Distance Formula

References

• Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of Physics. John Wiley & Sons.
• Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers. Cengage Learning.

Appendix

Here is the solution to the problem in a step-by-step format:

1. Define the problem: Two cars, Car A and Car B, are initially 30 km apart. Car A is traveling at a speed of $60 \text{ km/hr}$, while Car B is traveling at a speed of $90 \text{ km/hr}$.
2. Use the concept of relative motion to analyze the motion of the two cars. The relative speed of the two cars is $60 \text{ km/hr} + 90 \text{ km/hr} = 150 \text{ km/hr}$.
3. Use the distance formula to find the time it takes for the two cars to meet each other: $d = rt$.
4. Set up the equation: $30 = 150x$.
5. Solve for $x$: $x = \frac{30}{150} = \frac{1}{5}$.
6. Convert the time from hours to minutes: $\frac{1}{5} \times 60 = 12$.

By following these steps, we can solve the problem and determine the time it takes for the two cars to meet each other.