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 denote the average rate of speed on the first route as "x" (in mph), and the average rate of speed on the second route as "y" (in mph).
For the first route, we have the equation:
x = 400 miles / 8 hours
Simplifying this equation gives:
x = 50 mph
For the second route, we have the equation:
y = 420 miles / 7 hours
Simplifying this equation gives:
y = 60 mph
To calculate how much higher the average speed will be on the faster route, we need to find the difference between the two speeds:
Difference = y - x
Difference = 60 mph - 50 mph
Difference = 10 mph
Therefore, the average speed will be 10 mph higher on the faster route.
To find out how much higher your average speed will be on the faster route, we need to calculate the average speed for both routes.
Route 1: Time = 8 hours, Distance = 400 miles
Average Speed = Distance / Time = 400 miles / 8 hours = 50 miles per hour
Route 2: Time = 7 hours, Distance = 420 miles
Average Speed = Distance / Time = 420 miles / 7 hours = 60 miles per hour
To calculate the difference in average speeds, subtract the average speed of Route 1 from the average speed of Route 2:
Difference in Average Speeds = Average Speed of Route 2 - Average Speed of Route 1
= 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 calculate the average speed for each route, we can use the formula:
Average speed = Total distance / Total time.
First, let's calculate the average speed for the first route.
The distance is 400 miles, and the time is 8 hours.
So, the average speed for the first route is:
Average speed = 400 miles / 8 hours = 50 miles per hour.
Now, let's calculate the average speed for the second route.
The distance is 420 miles, and the time is 7 hours.
So, the average speed for the second route is:
Average speed = 420 miles / 7 hours = 60 miles per hour.
To find the difference in average speed between the two routes, we subtract the average speed of the first route from the average speed of the second route.
Difference in average speed = Average speed of second route - Average speed of first 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.