You are going to drive to another state for a vacation. One route will take 8 hours to drive 400 miles, and the other route will take 7 hours to drive 420 miles. You write two equations to try and figure out the average rate of speed you would travel on each route. How much higher will your average speed be on the faster route?
Let's represent the average speed on the first route as 'x' miles per hour, and the average speed on the second route as 'y' miles per hour.
According to the information given, the first route takes 8 hours to drive 400 miles. This can be written as the equation:
8 = 400/x
Similarly, the second route takes 7 hours to drive 420 miles. Representing this as an equation gives:
7 = 420/y
To find the average speed, we can use the formula: Average Speed = Total Distance / Total Time. Since both routes have different distances but take different amounts of time, we can use this formula to find the average speeds.
For the first route, the average speed can be calculated as:
Average Speed (Route 1) = 400/8
Average Speed (Route 1) = 50 miles per hour
For the second route, the average speed can be calculated as:
Average Speed (Route 2) = 420/7
Average Speed (Route 2) = 60 miles per hour
The average speed difference between the two routes is 60 - 50 = <<60-50=10>>10 miles per hour. Therefore, your average speed will be 10 miles per hour higher on the faster route.
To find the average speed, we need to divide the total distance traveled by the total time taken for each route.
For the first route, the equation can be written as:
Average Speed (in miles per hour) = Total Distance / Total Time
Average Speed (of the first route) = 400 miles / 8 hours
For the second route, the equation can be written as:
Average Speed (in miles per hour) = Total Distance / Total Time
Average Speed (of the second route) = 420 miles / 7 hours
Now, we can calculate the average speeds of each route:
Average Speed of the first route = 400 miles / 8 hours = 50 miles per hour
Average Speed of the second route = 420 miles / 7 hours = 60 miles per hour
To determine how much higher your average speed will be on the faster route, we need to compare the two average speeds:
Difference in Average Speed = Average Speed of the faster route - Average Speed of the slower route
Difference in Average Speed = 60 miles per hour - 50 miles per hour = 10 miles per hour
Therefore, your average speed will be 10 miles per hour higher on the faster route.
To determine the average rate of speed on each route, we can use the formula:
Average Speed = Total Distance / Total Time
For the first route, where it takes 8 hours to drive 400 miles:
Average Speed = 400 miles / 8 hours = 50 miles per hour
For the second route, where it takes 7 hours to drive 420 miles:
Average Speed = 420 miles / 7 hours = 60 miles per hour
To calculate how much higher your average speed will be on the faster route, we subtract the average speed of the slower route from the average speed of the faster route:
60 miles per hour - 50 miles per hour = 10 miles per hour
Therefore, your average speed will be 10 miles per hour higher on the faster route.