Harris Jogged $\frac{3}{5}$ Mile In $\frac{3}{25}$ Hour. What Is Harris's Rate In Miles Per Hour? Type Only The Number In The Box. $\square$ Miles Per Hour

Understanding the Problem

Harris jogged a certain distance in a given time, and we are asked to find his rate in miles per hour. To solve this problem, we need to understand the concept of rate and how it is calculated. The rate is defined as the distance traveled divided by the time taken.

Defining the Variables

Let's define the variables:

• Distance = $\frac{3}{5}$ mile
• Time = $\frac{3}{25}$ hour

Calculating the Rate

To calculate the rate, we need to divide the distance by the time. We can use the formula:

Rate = Distance ÷ Time

Substituting the values, we get:

Rate = $\frac{3}{5}$ ÷ $\frac{3}{25}$

Simplifying the Fraction

To simplify the fraction, we can multiply the numerator and denominator by the reciprocal of the other fraction. In this case, we can multiply by $\frac{25}{3}$:

Rate = $\frac{3}{5}$ × $\frac{25}{3}$ ÷ $\frac{3}{25}$

Canceling Out the Common Factors

We can cancel out the common factors in the numerator and denominator:

Rate = $\frac{3}{5}$ × $\frac{25}{3}$ ÷ $\frac{3}{25}$

= $\frac{3}{5}$ × $\frac{25}{1}$ ÷ $\frac{1}{25}$

Simplifying the Expression

Now, we can simplify the expression by canceling out the common factors:

Rate = $\frac{3}{5}$ × $\frac{25}{1}$ ÷ $\frac{1}{25}$

= $\frac{3}{5}$ × 25 ÷ 1

= $\frac{3}{5}$ × 25

= $\frac{75}{5}$

Final Answer

The final answer is $\boxed{15}$ miles per hour.

Conclusion

Q: What is the formula for calculating rate?

A: The formula for calculating rate is:

Rate = Distance ÷ Time

Q: How do I simplify a fraction when calculating rate?

A: To simplify a fraction when calculating rate, you can multiply the numerator and denominator by the reciprocal of the other fraction. For example, if you have the fraction $\frac{3}{5}$, you can multiply it by $\frac{5}{3}$ to get $\frac{15}{15}$, which simplifies to 1.

Q: What is the difference between rate and speed?

A: Rate and speed are often used interchangeably, but technically, rate refers to the distance traveled divided by the time taken, while speed refers to the distance traveled per unit of time. In this problem, we calculated Harris's rate in miles per hour, but in other contexts, we might calculate his speed in miles per hour.

Q: Can I use a calculator to calculate Harris's rate?

A: Yes, you can use a calculator to calculate Harris's rate. Simply enter the values for distance and time, and the calculator will give you the rate. However, it's also important to understand the underlying math and be able to calculate the rate by hand.

Q: What if the distance and time are given in different units?

A: If the distance and time are given in different units, you'll need to convert them to the same units before calculating the rate. For example, if the distance is given in kilometers and the time is given in hours, you'll need to convert the distance to kilometers and the time to hours before calculating the rate.

Q: Can I use this formula to calculate rate for other types of motion?

A: Yes, the formula for calculating rate can be used for other types of motion, such as walking, running, or even driving a car. As long as you have the distance traveled and the time taken, you can use this formula to calculate your rate.

Q: What if I'm given a rate and need to find the distance or time?

A: If you're given a rate and need to find the distance or time, you can use the formula:

Distance = Rate × Time

or

Time = Distance ÷ Rate

depending on which value you're trying to find.

Q: Can I use this formula to calculate rate for objects moving at different speeds?

A: Yes, the formula for calculating rate can be used for objects moving at different speeds. As long as you have the distance traveled and the time taken, you can use this formula to calculate the rate of any object, regardless of its speed.

Conclusion

In this article, we've answered some frequently asked questions about calculating Harris's rate. We've covered topics such as the formula for calculating rate, simplifying fractions, and using the formula for different types of motion. Whether you're a student or just looking for a refresher, we hope this article has been helpful in understanding how to calculate rate.