What were the average rates of Jackson and Trevor?
To find the average rates of Jackson and Trevor, we need to use the information provided in the data. Let's denote Trevor's average rate as x mph. According to the given information, Jackson's average rate was 3 mph faster than Trevor's, so we can represent Jackson's average rate as (x + 3) mph.
Using the formula for average rate: Average Rate = Total Distance / Total Time, and setting up the equation since both Jackson and Trevor biked for the same amount of time:
48 miles / (x + 3) mph = 36 miles / x mph
By cross-multiplying and solving for x, we get:
48x = 36(x + 3)
48x = 36x + 108
12x = 108
x = 9
Therefore, Trevor's average rate was 9 mph, and Jackson's average rate was (9 + 3) mph, which is 12 mph.
In summary, Jackson's average rate was 18 mph, and Trevor's average rate was 15 mph.
Finding Average Rates
When solving for the average rates of Jackson and Trevor, we first need to understand the relationship between their speeds. Jackson's average rate was 3 mph faster than Trevor's, indicating that there is a constant difference of 3 mph between their rates.
By setting up the equation and solving for x, we were able to determine Trevor's average rate as 9 mph and Jackson's average rate as 12 mph. This calculation allows us to clarify the given information and find the individual average rates of both bikers accurately.
Key Formula:
Average Rate = Total Distance / Total Time
This formula is essential in determining the speed at which an object travels over a given distance within a specific time frame. By applying this formula to the distances covered by Jackson and Trevor, we were able to calculate their respective average rates.
Understanding the Calculation:
The process of finding the average rates involved setting up an equation based on the information provided in the data. By equating the distances covered by each biker with their respective rates, we could establish a relationship that allowed us to solve for the unknown variable (Trevor's average rate).
Importance of Average Rates:
Average rates play a significant role in assessing and comparing the speeds of different objects or individuals. In the case of Jackson and Trevor's bicycle ride, their average rates provided crucial information about how fast each biker was traveling and allowed us to make an accurate comparison between them.
Overall, the calculation of Jackson and Trevor's average rates demonstrates the importance of understanding the relationship between distance, time, and speed in determining the rates at which objects or individuals travel. By applying basic formulas and mathematical concepts, we can analyze and interpret data related to motion and speed effectively.