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?

Question

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?

Options:
60 mph
10 mph
50 mph
20 mph

Answer 1

To find the average speed, we divide the distance traveled by the time taken. Let's calculate the average speed for each route:

Faster route:
Distance = 400 miles
Time = 8 hours
Average speed = Distance / Time = 400/8 = 50 mph

Slower route:
Distance = 420 miles
Time = 7 hours
Average speed = Distance / Time = 420/7 = 60 mph

Now, let's compare the average speeds of the two routes:

Difference in average speeds = 60 mph - 50 mph = 10 mph

Therefore, the average speed will be 10 mph higher on the faster route. The correct option is 10 mph.

Answer 2

To find the average rate of speed for each route, we can use the formula Speed = Distance / Time. Let's calculate the average speeds for both routes:

For the first route:
Speed = 400 miles / 8 hours = 50 mph

For the second route:
Speed = 420 miles / 7 hours = 60 mph

To determine how much higher the average speed will be 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 will be 10 mph higher on the faster route. The correct option is 10 mph.

Answer 3

To find the average rate of speed, we need to divide the distance traveled by the time it takes. Let's call the average speed of the first route "x" and the average speed of the second route "y". We can set up two equations based on the given information:

For the first route:
x = 400 miles / 8 hours

For the second route:
y = 420 miles / 7 hours

To compare the average speeds and determine the difference, we need to find the value of y - x.

Let's calculate the average speed for each route:

For the first route:
x = 400 miles / 8 hours
x = 50 mph

For the second route:
y = 420 miles / 7 hours
y = 60 mph

Now we can find the difference between the two average 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.