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 you average speed be on the faster route?
Let's denote the average rate of speed on the slower route as x miles per hour, and the average rate of speed on the faster route as y miles per hour.
The first equation can be written as:
400 = 8x
Simplifying this equation, we have:
x = 400/8
x = 50 mph
The second equation can be written as:
420 = 7y
Simplifying this equation, we have:
y = 420/7
y = 60 mph
To calculate the difference in average speed, we subtract the slower speed from the faster speed:
60 - 50 = 10 mph
Therefore, the average speed will be 10 mph higher on the faster route.