Question

Two equations are written to express how far a car can go when driving on different roads. On Road 1, the car can go 60 miles in 2 hours. On Road 2, the car can go 90 miles in 4 hours. Write an equation where y is the distance in miles and x is the time in hours to represent the motion of the faster car.(1 point

Answer 1

[AI-generated answer — Bot GPT 3.5]

The equation for the motion of the faster car can be written as:

y = mx + b

where:
m = slope (speed of the car)
b = y-intercept (starting point of the car)

To find the slope, we can use the formula:
m = (y2 - y1) / (x2 - x1)

Let's use the information given:
On Road 1, the car can go 60 miles in 2 hours. This can be represented as (x1, y1) = (2, 60).
On Road 2, the car can go 90 miles in 4 hours. This can be represented as (x2, y2) = (4, 90).

Substituting these values into the slope formula:
m = (90 - 60) / (4 - 2)
m = 30 / 2
m = 15

Now that we have the slope, we can choose any of the given points to find the y-intercept.
Let's use (x2, y2) = (4, 90):
90 = 15(4) + b
90 = 60 + b
b = 90 - 60
b = 30

Therefore, the equation representing the motion of the faster car is:
y = 15x + 30

Answer 2

so its

Answer 3

[AI-generated answer — Bot GPT 3.5]

y = 15x + 30

Answer 4

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?

Answer 5

[AI-generated answer — Bot GPT 3.5]

To find the average speed for each route, we 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:
Average speed of the first route = 400 miles / 8 hours = 50 miles per hour

For the second route, the distance is 420 miles and the time is 7 hours:
Average speed of the second route = 420 miles / 7 hours = 60 miles per hour

The average speed on the second route is 60 miles per hour - 50 miles per hour = 10 miles per hour higher than the first route.

Answer 6

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?

Answer 7

[AI-generated answer — Bot GPT 3.5]

To calculate the cost difference between Red Snaps and Blue Tarts, we need to find the total cost of each candy option.

For Red Snaps:
Cost per ounce of Red Snaps = $0.25
Total cost of 8 ounces of Red Snaps = 8 ounces * $0.25/ounce = $2.00

For Blue Tarts:
Cost per ounce of Blue Tarts = $0.30
Total cost of 8 ounces of Blue Tarts = 8 ounces * $0.30/ounce = $2.40

To find the cost difference, we subtract the cost of Red Snaps from the cost of Blue Tarts:
Cost difference = Total cost of Blue Tarts - Total cost of Red Snaps
Cost difference = $2.40 - $2.00
Cost difference = $0.40

Therefore, it would be $0.40 more expensive to get a bag of Blue Tarts instead of a bag of Red Snaps.

Answer 8

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

Answer 9

[AI-generated answer — Bot GPT 3.5]

To determine the day when you ran the fastest for the week, we need to compare the speed (distance/time) of each day.

On Monday, you ran 4 miles in 40 minutes. This can be represented as a speed of 4 miles / 40 minutes = 0.1 miles per minute.

On Wednesday, you ran 2 miles in 16 minutes. This can be represented as a speed of 2 miles / 16 minutes = 0.125 miles per minute.

To write an equation where y is the number of miles and x is the time in minutes for the day you ran the fastest, we need to determine which speed is faster.

Since 0.125 miles per minute is greater than 0.1 miles per minute, we can state that you ran fastest on Wednesday.

Therefore, the equation representing the day you ran the fastest for the week is:
y = 0.125x