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)
To determine the average speed, we can use the formula: average speed = distance / time.
For the first route, with a distance of 400 miles and a time of 8 hours, the average speed is:
average speed route 1 = 400 miles / 8 hours = 50 miles per hour.
For the second route, with a distance of 420 miles and a time of 7 hours, the average speed is:
average speed route 2 = 420 miles / 7 hours = 60 miles per hour.
The average speed on the faster route (route 2) is 60 miles per hour, while the average speed on the slower route (route 1) is 50 miles per hour.
Therefore, your average speed will be 10 miles per hour higher on the faster route.
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)
To determine the cost of the candy, we need to multiply the cost per ounce by the number of ounces.
For Red Snaps, the cost per ounce is $0.25 and you are buying 8 ounces, so the total cost of Red Snaps would be:
cost of Red Snaps = $0.25/ounce * 8 ounces = $2.00.
For Blue Tarts, the cost per ounce is $0.30 and you are still buying 8 ounces, so the total cost of Blue Tarts would be:
cost of Blue Tarts = $0.30/ounce * 8 ounces = $2.40.
The cost of Red Snaps is $2.00, while the cost of Blue Tarts is $2.40.
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)
Since the equation should represent the number of miles (y) as a function of time in minutes (x) on the day you ran the fastest for the week, we need to find the maximum value between the two workouts.
On Monday, you ran 4 miles in 40 minutes, so the equation for Monday's run is y = 4 miles and x = 40 minutes.
On Wednesday, you ran 2 miles in 16 minutes, so the equation for Wednesday's run is y = 2 miles and x = 16 minutes.
To find the maximum value, we need to compare the two equations:
y = max(4 miles, 2 miles)
x = min(40 minutes, 16 minutes)
Therefore, the equation that represents the number of miles (y) as a function of time in minutes (x) on the day you ran the fastest for the week would be:
y = max(4, 2) miles
x = min(40, 16) minutes
the options are
y=8x
y=0.125x
y=0.1x
y=10x
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=8x
y equals 8 x
y=0.125x
y equals 0.125x
y=10x
y equals 10 x
y=0.1x
To determine the average speed on each route, we need to divide the distance traveled by the time taken. Let's write the equations for each route.
For the first route:
Average speed = Distance / Time = 400 miles / 8 hours
For the second route:
Average speed = Distance / Time = 420 miles / 7 hours
To find out how much higher the average speed will be on the faster route, we need to compare the two average speeds.
First, let's calculate the average speed for each route:
Average speed for the first route = 400 miles / 8 hours = 50 miles/hour
Average speed for the second route = 420 miles / 7 hours ≈ 60 miles/hour
Now, let's compare the two average speeds:
The average speed on the faster route (second route) of 60 miles/hour is higher than the average speed on the first route (50 miles/hour) by 10 miles/hour.
So, the average speed will be 10 miles/hour higher on the faster route.
Since we are looking for the equation where y represents the number of miles and x represents the time in minutes for the day you ran the fastest for the week, we need to compare the two workouts and determine which one had the highest average speed.
On Monday, you ran 4 miles in 40 minutes, and on Wednesday, you ran 2 miles in 16 minutes.
To calculate the average speed, we divide the number of miles by the time in hours:
For Monday: Average speed = 4 miles / (40 minutes / 60 minutes per hour) = 6 miles per hour.
For Wednesday: Average speed = 2 miles / (16 minutes / 60 minutes per hour) = 7.5 miles per hour.
Since the average speed on Wednesday is higher than that of Monday, the equation y=7.5x represents the number of miles (y) as a function of time in minutes (x) on the day you ran the fastest for the week.