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?(1 point)Responses10 mph10 mph60 mph60 mph20 mph20 mph50 mph
To calculate the average speed, we use the formula:
Average speed = total distance / total time
For the first route, the average speed can be calculated as:
Average speed = 400 miles / 8 hours = 50 mph
For the second route, the average speed can be calculated as:
Average speed = 420 miles / 7 hours = 60 mph
The average speed on the faster route is 10 mph higher than the average speed on the slower route.
To calculate the average speed, we need to divide the total distance traveled by the total time taken. Let's assume the average speed of the first route is "x" miles per hour, and the average speed of the second route is "y" miles per hour.
The equation for the first route would be: 400 miles = 8 hours * x mph
The equation for the second route would be: 420 miles = 7 hours * y mph
To find the average speed for each route, we divide the distance traveled by the time taken:
Average speed of the first route = 400 miles / 8 hours = 50 mph
Average speed of the second route = 420 miles / 7 hours = 60 mph
The average speed on the faster route is 60 mph, and the average speed on the slower route is 50 mph.
Therefore, the average speed on the faster route is 10 mph higher.
To determine the average speed on each route, you can use the equation:
Average Speed = Total Distance / Total Time
For the first route, the distance is 400 miles and the time is 8 hours, so the equation becomes:
Average Speed1 = 400 miles / 8 hours
Simplifying the equation, we get:
Average Speed1 = 50 miles per hour
For the second route, the distance is 420 miles and the time is 7 hours, so the equation becomes:
Average Speed2 = 420 miles / 7 hours
Simplifying the equation, we get:
Average Speed2 = 60 miles per hour
To determine the difference in average speed between the two routes, we subtract the average speed of the slower route from the average speed of the faster route:
Difference = Average Speed2 - Average Speed1
Difference = 60 - 50
Difference = 10 miles per hour
Therefore, the average speed will be 10 miles per hour higher on the faster route.