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)
Responses
20 mph
20 mph
10 mph
10 mph
50 mph
50 mph
60 mph
To calculate the average rate of speed, 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 mph
For the second route, where it takes 7 hours to drive 420 miles:
Average speed = 420 miles / 7 hours = 60 mph
The average speed on the faster route is 60 mph, while the average speed on the slower route is 50 mph. Therefore, the average speed on the faster route is 10 mph higher.
To figure out the average rate of speed, you need to divide the distance traveled by the time it takes to travel that distance.
Let's denote the average speed on the first route as x mph. Using the equation for average speed, we can write:
x = distance/time
x = 400 miles/8 hours
x = 50 mph
Therefore, the average speed on the first route is 50 mph.
Now let's denote the average speed on the second route as y mph. Using the equation for average speed again, we can write:
y = distance/time
y = 420 miles/7 hours
y = 60 mph
Therefore, the average speed on the second route is 60 mph.
To determine how much higher the average speed is on the faster route, we subtract the average speed of the first route from the average speed of the second route:
60 mph - 50 mph = 10 mph
Therefore, the average speed is 10 mph higher on the faster route.