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)
10 mph
50 mph
60 mph
20 mph
To find the average rate of speed, we divide the total distance traveled by the total time taken.
For the first route, we have:
Average speed = distance/time = 400 miles / 8 hours = 50 mph
For the second route, we have:
Average speed = distance/time = 420 miles / 7 hours = 60 mph
The difference between the average speeds of the two routes is:
60 mph - 50 mph = 10 mph
Therefore, the average speed on the faster route is 10 mph higher.
A candy store sells different types of candy by the ounce. Red Snaps cost $0.25 per ounce, and Blue Tarts cost $0.30 per ounce. You decide to buy 8 ounces of candy to share with your friends. How much more expensive would it be to get a bag of Blue Tarts instead of a bag of Red Snaps?(1 point) Responses
$4.40
$0.40
$2.40
$2.00
The cost of Red Snaps per ounce is $0.25, so for 8 ounces, it would be:
8 ounces * $0.25 per ounce = $2.00
The cost of Blue Tarts per ounce is $0.30, so for 8 ounces, it would be:
8 ounces * $0.30 per ounce = $2.40
To calculate the difference, we subtract the cost of the Red Snaps from the cost of the Blue Tarts:
$2.40 - $2.00 = $0.40
Therefore, it would be $0.40 more expensive to get a bag of Blue Tarts instead of a bag of Red Snaps.
You are training twice a week for a race. On Monday, you go 4 miles in 40 minutes. Then on Wednesday you go 2 miles in 16 minutes. Write an equation where y is the number of miles and x is the time in minutes for the day you ran the fastest for the week.(1 point)
y = 0.1x
y = 0.125x
y = 10x
y = 8x
To determine which day you ran the fastest, we need to find the highest speed (in miles per minute). We can calculate this by dividing the number of miles by the time taken.
For Monday, the speed is 4 miles / 40 minutes = 0.1 miles per minute.
For Wednesday, the speed is 2 miles / 16 minutes = 0.125 miles per minute.
Since we are looking for the day you ran the fastest, we want to maximize y, the number of miles, for a given x, the time in minutes.
The equation that represents the relationship between the number of miles (y) and the time in minutes (x) for the day you ran the fastest is:
y = 0.125x
To compare the average speed on each route, we need to calculate the speed using the given information.
Let's start by calculating the average speed on the first route:
Average speed = Total distance / Total time
Average speed 1 = 400 miles / 8 hours
Average speed 1 = 50 mph (miles per hour)
Now let's calculate the average speed on the second route:
Average speed 2 = 420 miles / 7 hours
Average speed 2 = 60 mph (miles per hour)
To find out how much higher your average speed will be on the faster route, we subtract the average speed on the slower route from the average speed on the faster route:
Difference in average speed = Average speed 2 - Average speed 1
Difference in average speed = 60 mph - 50 mph
Difference in average speed = 10 mph
Therefore, the average speed will be 10 mph higher on the faster route.
To determine the average rate of speed on each route, we need to divide the total distance traveled by the time taken on that route.
For the first route, the distance is 400 miles and the time taken is 8 hours. So, the average speed on the first route can be calculated using the equation: Average Speed = Distance / Time = 400 miles / 8 hours = 50 miles per hour.
For the second route, the distance is 420 miles and the time taken is 7 hours. Using the same equation, the average speed on the second route is: Average Speed = Distance / Time = 420 miles / 7 hours = 60 miles per hour.
Therefore, the average speed on the faster route is 60 miles per hour, while the average speed on the slower route is 50 miles per hour.
To determine how much higher the average speed will be on the faster route, we subtract the average speed of the slower route (50 mph) from the average speed of the faster route (60 mph).
So, the difference in average speeds is 60 mph - 50 mph = 10 mph.
Therefore, the average speed will be 10 mph higher on the faster route.