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 speed on the first route as v1 (in miles per hour) and the average speed on the second route as v2 (also in miles per hour).
According to the given information, the first route is 400 miles long and takes 8 hours to drive, so the equation for the first route is:
v1 = 400/8
Simplifying this equation, we get:
v1 = 50 mph
Similarly, the second route is 420 miles long and takes 7 hours to drive, so the equation for the second route is:
v2 = 420/7
Simplifying this equation, we get:
v2 = 60 mph
The average speed on the faster route (v2) is 60 mph, while the average speed on the slower route (v1) is 50 mph. Therefore, the average speed on the faster route is 10 mph higher than the average speed on the slower route.
To find the average speed on each route, we need to divide the total distance by the total time taken for each route.
Let's first calculate the average speed for the first route, which takes 8 hours to drive 400 miles:
Average speed = distance / time
Average speed = 400 miles / 8 hours
Average speed = 50 miles per hour
Now let's calculate the average speed for the second route, which takes 7 hours to drive 420 miles:
Average speed = distance / time
Average speed = 420 miles / 7 hours
Average speed = 60 miles per hour
To find the difference in average speeds, we subtract the average speed of the slower route from the average speed of the faster route:
Difference in average speeds = Average speed of faster route - Average speed of slower route
Difference in average speeds = 60 miles per hour - 50 miles per hour
Difference in average speeds = 10 miles per hour
The average speed will be 10 miles per hour higher on the faster route.
To determine the average speed of each route, we need to divide the total distance traveled by the time taken to travel that distance.
For the first route, the equation is: average speed = total distance / time taken.
Given that it takes 8 hours to drive 400 miles on the first route, we can calculate the average speed:
average speed = 400 miles / 8 hours = 50 mph.
Similarly, for the second route, the equation is: average speed = total distance / time taken.
Given that it takes 7 hours to drive 420 miles on the second route, we can calculate the average speed:
average speed = 420 miles / 7 hours = 60 mph.
To determine how much higher the average speed is on the faster route, we can subtract the slower average speed from the faster average speed:
Difference in average speed = faster average speed - slower average speed
Difference in average speed = 60 mph - 50 mph = 10 mph.
Therefore, the average speed on the faster route is 10 mph higher than the average speed on the slower route.