Jayne Needs To Drive 470 Miles To Reach Milwaukee. Suppose He Drives At A Constant Speed Of 50 Miles Per Hour. Which Function Represents Jayne's Distance In Miles From Milwaukee In Terms Of The Number Of Hours He Drives?A. Y = 420 X Y = 420x Y = 420 X B.

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When it comes to calculating distance, speed, and time, it's essential to understand the relationship between these three variables. In this problem, we're given Jayne's initial distance from Milwaukee, which is 470 miles, and his constant speed of 50 miles per hour. We need to find a function that represents Jayne's distance in miles from Milwaukee in terms of the number of hours he drives.

Defining the Variables

Let's define the variables involved in this problem:

  • Distance (d): The distance Jayne is from Milwaukee in miles.
  • Speed (s): Jayne's constant speed of 50 miles per hour.
  • Time (t): The number of hours Jayne drives.

The Relationship Between Distance, Speed, and Time

The relationship between distance, speed, and time is given by the formula:

d = s × t

This formula states that the distance traveled is equal to the product of the speed and the time.

Representing the Function

Since we want to find a function that represents Jayne's distance in miles from Milwaukee in terms of the number of hours he drives, we can use the formula d = s × t. However, we need to express the distance in terms of the time, which is the number of hours Jayne drives.

Let's substitute the given values into the formula:

  • s = 50 miles per hour (Jayne's constant speed)
  • t = x hours (the number of hours Jayne drives)

Substituting these values into the formula, we get:

d = 50 × x

Simplifying the equation, we get:

d = 50x

This is the function that represents Jayne's distance in miles from Milwaukee in terms of the number of hours he drives.

Comparing with the Options

Now that we have the function d = 50x, let's compare it with the given options:

  • A. y = 420x
  • B. y = 50x

Comparing the two options, we can see that option B, y = 50x, matches our derived function.

Conclusion

In this problem, we used the formula d = s × t to find a function that represents Jayne's distance in miles from Milwaukee in terms of the number of hours he drives. We substituted the given values into the formula and simplified the equation to get the function d = 50x. This function matches option B, y = 50x, which is the correct answer.

Final Answer

The final answer is option B, y = 50x.

Additional Information

  • The initial distance from Milwaukee is 470 miles.
  • Jayne's constant speed is 50 miles per hour.
  • The function d = 50x represents Jayne's distance in miles from Milwaukee in terms of the number of hours he drives.

Mathematical Concepts

  • Distance, speed, and time are related by the formula d = s × t.
  • The function d = 50x represents a linear relationship between distance and time.

Real-World Applications

  • This problem can be applied to real-world scenarios, such as calculating the distance traveled by a car or a plane.
  • Understanding the relationship between distance, speed, and time is essential in various fields, including physics, engineering, and transportation.
    Q&A: Understanding Distance, Speed, and Time =====================================================

In the previous article, we discussed the problem of Jayne driving 470 miles to reach Milwaukee at a constant speed of 50 miles per hour. We derived a function that represents Jayne's distance in miles from Milwaukee in terms of the number of hours he drives. In this article, we'll answer some frequently asked questions related to this problem.

Q: What is the formula for distance, speed, and time?

A: The formula for distance, speed, and time is:

d = s × t

Where:

  • d is the distance traveled
  • s is the speed
  • t is the time

Q: How do I use the formula to find the distance traveled?

A: To find the distance traveled, you need to multiply the speed by the time. For example, if the speed is 50 miles per hour and the time is 2 hours, the distance traveled would be:

d = 50 × 2 d = 100 miles

Q: What if I want to find the time it takes to travel a certain distance?

A: To find the time it takes to travel a certain distance, you need to divide the distance by the speed. For example, if the distance is 100 miles and the speed is 50 miles per hour, the time it takes to travel that distance would be:

t = d ÷ s t = 100 ÷ 50 t = 2 hours

Q: What if I want to find the speed required to travel a certain distance in a certain time?

A: To find the speed required to travel a certain distance in a certain time, you need to divide the distance by the time. For example, if the distance is 100 miles and the time is 2 hours, the speed required to travel that distance would be:

s = d ÷ t s = 100 ÷ 2 s = 50 miles per hour

Q: Can I use the formula to find the distance traveled if I know the speed and time, but the time is in minutes?

A: Yes, you can use the formula to find the distance traveled if you know the speed and time, but the time is in minutes. You just need to convert the time from minutes to hours by dividing it by 60. For example, if the speed is 50 miles per hour and the time is 120 minutes, the distance traveled would be:

t = 120 ÷ 60 t = 2 hours d = s × t d = 50 × 2 d = 100 miles

Q: Can I use the formula to find the time it takes to travel a certain distance if I know the speed and distance, but the speed is in kilometers per hour?

A: Yes, you can use the formula to find the time it takes to travel a certain distance if you know the speed and distance, but the speed is in kilometers per hour. You just need to convert the speed from kilometers per hour to miles per hour by multiplying it by 0.621371. For example, if the distance is 100 miles and the speed is 80 kilometers per hour, the time it takes to travel that distance would be:

s = 80 × 0.621371 s = 49.7 miles per hour t = d ÷ s t = 100 ÷ 49.7 t = 2.01 hours

Conclusion

In this article, we answered some frequently asked questions related to the problem of Jayne driving 470 miles to reach Milwaukee at a constant speed of 50 miles per hour. We discussed the formula for distance, speed, and time, and how to use it to find the distance traveled, time it takes to travel a certain distance, and speed required to travel a certain distance in a certain time. We also discussed how to convert between different units of time and speed.