Compare Proportions from Graphs & Equations Quick Check
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An illustration shows quadrant one of a coordinate plane where the x-axis and y-axis range from 0 to 6 in increments of 1. The y-axis is titled distance in feet and the x-axis is titled time in seconds. A solid line, labeled A, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 3 comma 6 right parenthesis. A dotted line, labeled B, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 6 comma 6 right parenthesis. A dashed line, labeled C, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 6 comma 3 right parenthesis.
An illustration shows quadrant one of a coordinate plane where the x-axis and y-axis range from 0 to 6 in increments of 1. The y-axis is titled total cost in dollars and the x-axis is titled number of markers. A solid line, labeled A, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 3 comma 6 right parenthesis. A dotted line, labeled B, passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 6 comma 3 right parenthesis.
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?(1 point)
Responses
10 mph
10 mph
60 mph
60 mph
20 mph
20 mph
50 mph
50 mph
To find the cost difference between a bag of Blue Tarts and a bag of Red Snaps, we need to calculate the difference in price per ounce and multiply it by the number of ounces.
The cost of 8 ounces of Red Snaps is 8 ounces * $0.25/ounce = $2.00.
The cost of 8 ounces of Blue Tarts is 8 ounces * $0.30/ounce = $2.40.
The price difference is $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.
The correct answer is $0.40.
To find the average speed, we divide the distance traveled by the time taken for each route.
For the first route, the average speed is 400 miles / 8 hours = 50 mph.
For the second route, the average speed is 420 miles / 7 hours = 60 mph.
The average speed on the faster route (second route) is 60 mph - 50 mph = 10 mph higher.
Therefore, the correct answer is 10 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
$4.40
$4.40
$2.40
$2.40
$0.40
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 find the equation for the day you ran the fastest for the week, we need to compare the speeds at which you ran on Monday and Wednesday.
On Monday, you ran 4 miles in 40 minutes, so your speed was 4 miles / 40 minutes = 0.1 miles/minute.
On Wednesday, you ran 2 miles in 16 minutes, so your speed was 2 miles / 16 minutes = 0.125 miles/minute.
Since we want to find the equation where y is the number of miles and x is the time in minutes, the equation for the fastest day's speed would be:
y = 0.125x
So, the correct equation is: y equals 0.125x.
To find the average speed, we need to divide the total distance traveled by the time it takes to travel that distance.
For the first route, the equation would be:
Average speed = 400 miles / 8 hours = 50 mph
For the second route, the equation would be:
Average speed = 420 miles / 7 hours = 60 mph
To find the difference in average speeds, we 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. The correct answer is:
10 mph
To find the average speed for each route, we need to divide the distance traveled by the time taken on each route.
For the first route, the equation can be written as:
Average Speed = Distance / Time
Average Speed = 400 miles / 8 hours
Average Speed = 50 miles per hour
For the second route, the equation can be written as:
Average Speed = Distance / Time
Average Speed = 420 miles / 7 hours
Average Speed = 60 miles per hour
Now we need to find the difference in average speed between the two routes.
The average speed on the faster route is 60 miles per hour, and the average speed on the slower route is 50 miles per hour.
To find the difference, we subtract the average speed of the slower route from the average speed of the faster route:
Difference = Faster route average speed - Slower route average speed
Difference = 60 mph - 50 mph
Difference = 10 mph
Therefore, the average speed will be 10 mph higher on the faster route compared to the slower route.