A Family Is Driving 550 Miles To Their Grandmother's House. They Have Already Driven 350 Miles. Which Equation Shows The Rate, R R R , In Miles Per Hour, The Family Must Drive To Reach Their Grandmother's House In 4 Hours?A. $4r + 350 =

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Introduction

When planning a road trip, it's essential to consider the distance to be covered, the time available, and the speed required to reach the destination on time. In this scenario, a family is driving 550 miles to their grandmother's house and has already covered 350 miles. To determine the required speed to reach their destination in 4 hours, we need to use a mathematical equation that represents the relationship between distance, speed, and time.

Understanding the Problem

The family has already driven 350 miles out of the total 550 miles. This means they have 200 miles left to cover (550 - 350 = 200). They want to reach their grandmother's house in 4 hours. To find the required speed, we need to use the formula:

Speed = Distance / Time

In this case, the distance is 200 miles, and the time is 4 hours. We can plug these values into the formula to find the required speed.

The Equation

The equation that represents the required speed, r, in miles per hour, is:

r = 200 / 4

Simplifying the equation, we get:

r = 50

However, this is not the only equation that can represent the required speed. We can also use the equation:

4r + 350 = 550

This equation represents the total distance (550 miles) as the sum of the distance already covered (350 miles) and the distance left to cover (200 miles). The variable r represents the required speed, and the equation states that the product of 4 and r (the speed) plus 350 (the distance already covered) is equal to 550 (the total distance).

Analyzing the Equation

Let's analyze the equation 4r + 350 = 550. We can start by subtracting 350 from both sides of the equation to isolate the term with the variable r:

4r = 200

Next, we can divide both sides of the equation by 4 to solve for r:

r = 200 / 4

Simplifying the equation, we get:

r = 50

This confirms that the required speed is 50 miles per hour.

Conclusion

In conclusion, the equation that shows the rate, r, in miles per hour, the family must drive to reach their grandmother's house in 4 hours is:

4r + 350 = 550

This equation represents the total distance as the sum of the distance already covered and the distance left to cover. By solving for r, we can determine the required speed to reach the destination on time.

Frequently Asked Questions

  • What is the required speed to reach the grandmother's house in 4 hours?
  • How can we use the equation 4r + 350 = 550 to find the required speed?
  • What is the relationship between distance, speed, and time in this scenario?

Answers

  • The required speed is 50 miles per hour.
  • We can use the equation 4r + 350 = 550 to find the required speed by solving for r.
  • The relationship between distance, speed, and time is represented by the formula: Speed = Distance / Time.

Additional Resources

  • For more information on calculating speed and distance, visit the following websites:

Q&A: Calculating Speed and Distance

Q: What is the required speed to reach the grandmother's house in 4 hours?

A: The required speed is 50 miles per hour.

Q: How can we use the equation 4r + 350 = 550 to find the required speed?

A: We can use the equation 4r + 350 = 550 to find the required speed by solving for r. First, subtract 350 from both sides of the equation to get 4r = 200. Then, divide both sides of the equation by 4 to get r = 50.

Q: What is the relationship between distance, speed, and time in this scenario?

A: The relationship between distance, speed, and time is represented by the formula: Speed = Distance / Time. In this scenario, the distance is 200 miles, and the time is 4 hours. Therefore, the required speed is 50 miles per hour.

Q: How can we calculate the required speed if we know the distance and time?

A: We can calculate the required speed by using the formula: Speed = Distance / Time. For example, if the distance is 200 miles and the time is 4 hours, the required speed is 50 miles per hour.

Q: What if we want to calculate the time it will take to cover a certain distance at a certain speed?

A: We can use the formula: Time = Distance / Speed. For example, if the distance is 200 miles and the speed is 50 miles per hour, the time it will take to cover the distance is 4 hours.

Q: How can we use the equation 4r + 350 = 550 to calculate the required speed if we know the distance and time?

A: We can use the equation 4r + 350 = 550 to calculate the required speed by solving for r. First, subtract 350 from both sides of the equation to get 4r = 200. Then, divide both sides of the equation by 4 to get r = 50.

Q: What if we want to calculate the distance it will take to cover at a certain speed in a certain amount of time?

A: We can use the formula: Distance = Speed x Time. For example, if the speed is 50 miles per hour and the time is 4 hours, the distance it will take to cover is 200 miles.

Q: How can we use the equation 4r + 350 = 550 to calculate the distance it will take to cover at a certain speed in a certain amount of time?

A: We can use the equation 4r + 350 = 550 to calculate the distance it will take to cover at a certain speed in a certain amount of time by solving for r. First, subtract 350 from both sides of the equation to get 4r = 200. Then, divide both sides of the equation by 4 to get r = 50. Finally, use the formula: Distance = Speed x Time to calculate the distance it will take to cover.

Additional Resources

  • For more information on calculating speed and distance, visit the following websites: