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
10 mph
10 mph
60 mph
60 mph
20 mph
20 mph
50 mph
To figure out the average rate of speed for each route, you can use the formula: average speed = total distance / total time.
For the first route, the distance is 400 miles and the time is 8 hours. The average speed can be calculated as:
average speed = 400 miles / 8 hours = 50 mph.
For the second route, the distance is 420 miles and the time is 7 hours. The average speed can be calculated as:
average speed = 420 miles / 7 hours = 60 mph.
Therefore, the average speed on the faster route (60 mph) is 10 mph higher than the average speed on the slower route (50 mph).
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
$2.00
$2.00
$0.40
$0.40
$4.40
$4.40
$2.40
To calculate how much more expensive it would be to get a bag of Blue Tarts instead of Red Snaps, you need to find the difference in price per ounce and multiply it by the number of ounces you plan to buy.
The price per ounce for Red Snaps is $0.25 and for Blue Tarts is $0.30.
The difference in price per ounce is $0.30 - $0.25 = $0.05.
As you plan to buy 8 ounces of candy, you multiply the price difference per ounce by 8:
$0.05 x 8 = $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)
Responses
y=10x
y equals 10 x
y=0.125x
y equals 0.125x
y=0.1x
y equals 0.1x
y=8x
To write the 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, we need to compare the rate at which you covered the distance on Monday and Wednesday.
On Monday, you ran 4 miles in 40 minutes. The rate can be calculated as:
Rate = Distance / Time = 4 miles / 40 minutes = 0.1 miles per minute.
On Wednesday, you ran 2 miles in 16 minutes. The rate can be calculated as:
Rate = Distance / Time = 2 miles / 16 minutes = 0.125 miles per minute.
Since we are looking for the day when you ran the fastest, we can see that Wednesday had the higher rate of 0.125 miles per minute.
Therefore, the equation for the day you ran the fastest for the week is y = 0.125x, where y represents the number of miles and x represents the time in minutes.
To calculate the average speed, you need to divide the total distance traveled by the total time taken.
For the first route, the equation would be:
Average Speed of First Route = Distance / Time
Average Speed of First Route = 400 miles / 8 hours
Simplifying the equation:
Average Speed of First Route = 50 miles per hour
For the second route, the equation would be:
Average Speed of Second Route = Distance / Time
Average Speed of Second Route = 420 miles / 7 hours
Simplifying the equation:
Average Speed of Second Route = 60 miles per hour
To find the difference in average speeds, subtract the average speed of the slower route from the average speed of the faster route:
60 mph - 50 mph = 10 mph
Therefore, the average speed on the faster route will be 10 mph higher than the average speed on the slower route.