Each Week, Rosario Drives To An Ice-skating Rink That Is 60 Miles Away. The Round Trip Takes 2.75 Hours. If He Averages 55 Miles Per Hour On His Way To The Rink, Which Equation Can Be Used To Find { X $}$, The Number Of Miles Per Hour He

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Introduction

In this article, we will delve into a real-world problem involving distance, speed, and time. We will use mathematical concepts to create an equation that can be used to find the number of miles per hour Rosario drives on his way back from the ice-skating rink. This problem is a great example of how mathematics can be applied to everyday situations.

Given Information

  • The distance to the ice-skating rink is 60 miles.
  • The round trip takes 2.75 hours.
  • Rosario averages 55 miles per hour on his way to the rink.

Creating the Equation

To create the equation, we need to use the formula:

Distance = Speed × Time

We know that the distance to the rink is 60 miles, and Rosario averages 55 miles per hour on his way to the rink. We can use this information to find the time it takes for Rosario to drive to the rink:

Time = Distance ÷ Speed

Plugging in the values, we get:

Time = 60 miles ÷ 55 miles/hour

Time = 1.09 hours

Now that we have the time it takes for Rosario to drive to the rink, we can use the formula:

Total Distance = 2 × Distance to the Rink

Since the round trip takes 2.75 hours, we can set up the equation:

2.75 hours = 2 × 1.09 hours + x

where x is the time it takes for Rosario to drive back from the rink.

Simplifying the Equation

We can simplify the equation by multiplying both sides by 2:

5.5 hours = 2.18 hours + 2x

Now, we can isolate the term 2x by subtracting 2.18 hours from both sides:

3.32 hours = 2x

Finally, we can divide both sides by 2 to solve for x:

x = 1.66 hours

Converting Time to Speed

Now that we have the time it takes for Rosario to drive back from the rink, we can use the formula:

Speed = Distance ÷ Time

Plugging in the values, we get:

Speed = 60 miles ÷ 1.66 hours

Speed = 36.14 miles/hour

Conclusion

In this article, we used mathematical concepts to create an equation that can be used to find the number of miles per hour Rosario drives on his way back from the ice-skating rink. We started by using the formula:

Distance = Speed × Time

to find the time it takes for Rosario to drive to the rink. We then used the formula:

Total Distance = 2 × Distance to the Rink

to set up the equation:

2.75 hours = 2 × 1.09 hours + x

We simplified the equation by multiplying both sides by 2 and isolating the term 2x. Finally, we divided both sides by 2 to solve for x and converted the time to speed using the formula:

Speed = Distance ÷ Time

The final answer is 36.14 miles/hour.

Additional Information

  • The equation we created can be used to find the number of miles per hour Rosario drives on his way back from the ice-skating rink.
  • The problem can be solved using algebraic manipulations and mathematical formulas.
  • The solution involves using the formula:

Distance = Speed × Time

to find the time it takes for Rosario to drive to the rink, and then using the formula:

Total Distance = 2 × Distance to the Rink

to set up the equation.

References

  • [1] "Algebra and Trigonometry" by Michael Sullivan
  • [2] "Mathematics for the Nonmathematician" by Morris Kline

Keywords

  • Distance
  • Speed
  • Time
  • Algebra
  • Trigonometry
  • Mathematics
  • Problem-solving
  • Equation
  • Solution
    Frequently Asked Questions: Understanding Distance, Speed, and Time ====================================================================

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

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

Distance = Speed × Time

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

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

A: To find the distance traveled, you can use the formula:

Distance = Speed × Time

by plugging in the values for speed and time.

Q: What if I know the distance and speed, but not the time? How can I find the time?

A: If you know the distance and speed, but not the time, you can use the formula:

Time = Distance ÷ Speed

to find the time.

Q: What if I know the distance and time, but not the speed? How can I find the speed?

A: If you know the distance and time, but not the speed, you can use the formula:

Speed = Distance ÷ Time

to find the speed.

Q: Can I use the formula to find the speed if I know the distance and time, but the speed is not constant?

A: Yes, you can use the formula to find the speed if you know the distance and time, but the speed is not constant. However, you will need to use the average speed, which is the total distance divided by the total time.

Q: How can I use the formula to find the time if I know the distance and speed, but the speed is not constant?

A: If you know the distance and speed, but the speed is not constant, you can use the formula:

Time = Distance ÷ Average Speed

to find the time.

Q: What is the difference between average speed and instantaneous speed?

A: Average speed is the total distance divided by the total time, while instantaneous speed is the speed at a specific point in time.

Q: Can I use the formula to find the distance if I know the speed and time, but the distance is not constant?

A: Yes, you can use the formula to find the distance if you know the speed and time, but the distance is not constant. However, you will need to use the average distance, which is the total distance divided by the total time.

Q: How can I use the formula to find the time if I know the distance and speed, but the distance is not constant?

A: If you know the distance and speed, but the distance is not constant, you can use the formula:

Time = Total Distance ÷ Average Speed

to find the time.

Q: What if I know the distance, speed, and time, but I want to find the distance traveled at a specific point in time? How can I do this?

A: If you know the distance, speed, and time, but you want to find the distance traveled at a specific point in time, you can use the formula:

Distance = Speed × Time

and plug in the values for speed and time.

Q: Can I use the formula to find the speed if I know the distance and time, but the speed is not constant, and the distance is not constant?

A: Yes, you can use the formula to find the speed if you know the distance and time, but the speed is not constant, and the distance is not constant. However, you will need to use the average speed, which is the total distance divided by the total time.

Conclusion

In this article, we have answered some frequently asked questions about distance, speed, and time. We have shown how to use the formula:

Distance = Speed × Time

to find the distance traveled, the time, and the speed. We have also discussed how to use the formula when the speed and distance are not constant. We hope that this article has been helpful in understanding the relationship between distance, speed, and time.

Additional Information

  • The formula:

Distance = Speed × Time

can be used to find the distance traveled, the time, and the speed.

  • The average speed is the total distance divided by the total time.
  • The instantaneous speed is the speed at a specific point in time.
  • The formula can be used to find the distance traveled at a specific point in time.

References

  • [1] "Algebra and Trigonometry" by Michael Sullivan
  • [2] "Mathematics for the Nonmathematician" by Morris Kline

Keywords

  • Distance
  • Speed
  • Time
  • Algebra
  • Trigonometry
  • Mathematics
  • Problem-solving
  • Equation
  • Solution
  • Average speed
  • Instantaneous speed