Vik Wrote The Equation $470 \cdot H = 3,008$, Where $h$ Is The Number Of Hours It Took A Plane Flying At A Constant Speed Of 470 Miles Per Hour To Travel 3,008 Miles. Solve For $ H H H [/tex].

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Introduction

In the world of mathematics, equations are used to represent real-world problems and relationships. One such equation is the one written by Vik, which represents the time it took for a plane to travel a certain distance at a constant speed. In this article, we will solve for the unknown variable, h, which represents the number of hours it took for the plane to travel 3,008 miles at a speed of 470 miles per hour.

The Equation

The equation written by Vik is:

470â‹…h=3,008470 \cdot h = 3,008

Where h is the number of hours it took for the plane to travel 3,008 miles at a speed of 470 miles per hour.

Understanding the Problem

To solve for h, we need to isolate the variable h on one side of the equation. This can be done by dividing both sides of the equation by 470, which is the coefficient of h.

Step-by-Step Solution

Step 1: Divide Both Sides by 470

To isolate h, we need to divide both sides of the equation by 470. This will give us:

h=3,008470h = \frac{3,008}{470}

Step 2: Simplify the Fraction

To simplify the fraction, we can divide the numerator (3,008) by the denominator (470). This will give us:

h=6.4h = 6.4

Step 3: Interpret the Result

The result of the calculation is h = 6.4. This means that it took the plane 6.4 hours to travel 3,008 miles at a speed of 470 miles per hour.

Conclusion

In this article, we solved for the unknown variable h in the equation $470 \cdot h = 3,008$. By dividing both sides of the equation by 470, we isolated h and simplified the fraction to get the result h = 6.4. This means that it took the plane 6.4 hours to travel 3,008 miles at a speed of 470 miles per hour.

Real-World Applications

The concept of solving for time is used in many real-world applications, such as:

  • Flight Planning: Pilots use mathematical equations to plan their flight routes and estimate the time it will take to reach their destination.
  • Traffic Management: Traffic engineers use mathematical equations to optimize traffic flow and reduce congestion on roads.
  • Logistics: Companies use mathematical equations to optimize their supply chain and reduce delivery times.

Mathematical Concepts

The concept of solving for time is based on the following mathematical concepts:

  • Algebra: Algebra is the branch of mathematics that deals with the study of variables and their relationships.
  • Equations: Equations are mathematical statements that express the equality of two expressions.
  • Fractions: Fractions are mathematical expressions that represent a part of a whole.

Tips and Tricks

Here are some tips and tricks to help you solve for time:

  • Use a calculator: A calculator can help you simplify fractions and calculate the result quickly.
  • Check your units: Make sure that your units are consistent, such as hours, minutes, or seconds.
  • Use a formula: If you are given a formula, use it to solve for the unknown variable.

Practice Problems

Here are some practice problems to help you practice solving for time:

  • Problem 1: A car travels at a speed of 60 miles per hour. If it travels for 4 hours, how many miles does it travel?
  • Problem 2: A plane travels at a speed of 500 miles per hour. If it travels for 2 hours, how many miles does it travel?
  • Problem 3: A bike travels at a speed of 20 miles per hour. If it travels for 3 hours, how many miles does it travel?

Answer Key

Here are the answers to the practice problems:

  • Problem 1: 240 miles
  • Problem 2: 1,000 miles
  • Problem 3: 60 miles
    Frequently Asked Questions: Solving for Time =====================================================

Q: What is the formula to solve for time?

A: The formula to solve for time is:

t=drt = \frac{d}{r}

Where t is the time, d is the distance, and r is the rate (speed).

Q: How do I use the formula to solve for time?

A: To use the formula, you need to plug in the values for distance and rate. For example, if you know that a car travels 240 miles in 4 hours, you can use the formula to solve for the rate:

r=dt=2404=60r = \frac{d}{t} = \frac{240}{4} = 60

Q: What if I have a variable in the equation?

A: If you have a variable in the equation, you can use algebra to solve for the variable. For example, if you have the equation:

470â‹…h=3,008470 \cdot h = 3,008

You can solve for h by dividing both sides of the equation by 470:

h=3,008470=6.4h = \frac{3,008}{470} = 6.4

Q: How do I check my units?

A: To check your units, make sure that your units are consistent. For example, if you are solving for time in hours, make sure that your rate is in miles per hour.

Q: What if I have a fraction in the equation?

A: If you have a fraction in the equation, you can simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD). For example, if you have the fraction:

3,008470\frac{3,008}{470}

You can simplify the fraction by dividing both the numerator and denominator by 2:

1,504235\frac{1,504}{235}

Q: How do I use a calculator to solve for time?

A: To use a calculator to solve for time, you can plug in the values for distance and rate, and then divide the distance by the rate. For example, if you know that a car travels 240 miles in 4 hours, you can use a calculator to solve for the rate:

r=dt=2404=60r = \frac{d}{t} = \frac{240}{4} = 60

Q: What if I have a complex equation?

A: If you have a complex equation, you can use algebra to solve for the variable. For example, if you have the equation:

470â‹…h+200=3,008470 \cdot h + 200 = 3,008

You can solve for h by subtracting 200 from both sides of the equation, and then dividing both sides of the equation by 470:

h=3,008−200470=2,808470=6h = \frac{3,008 - 200}{470} = \frac{2,808}{470} = 6

Q: How do I use a formula to solve for time in a real-world application?

A: To use a formula to solve for time in a real-world application, you need to identify the variables in the equation and plug in the values. For example, if you are planning a road trip and you know the distance to your destination and the speed limit, you can use the formula to solve for the time:

t=dr=24060=4t = \frac{d}{r} = \frac{240}{60} = 4

Q: What are some common mistakes to avoid when solving for time?

A: Some common mistakes to avoid when solving for time include:

  • Not checking units: Make sure that your units are consistent.
  • Not simplifying fractions: Simplify fractions by dividing the numerator and denominator by their greatest common divisor (GCD).
  • Not using a calculator: Use a calculator to simplify calculations.
  • Not checking the equation: Check the equation to make sure that it is correct.

Conclusion

Solving for time is an important concept in mathematics and has many real-world applications. By understanding the formula and using algebra, you can solve for time in a variety of situations. Remember to check your units, simplify fractions, and use a calculator to simplify calculations.