Question
A machine can fill 5,400 bottles in 3 hours. How many bottles can it fill in 8 hours?(1 point)
bottles
To find out how many bottles the machine can fill in 8 hours, we can use a proportion.
We know that the machine can fill 5,400 bottles in 3 hours.
Let's set up the proportion:
5,400 bottles / 3 hours = x bottles / 8 hours
To solve for x, we can cross multiply:
3 * x = 5,400 * 8
3x = 43,200
Now, we can divide both sides by 3 to find x:
x = 43,200 / 3
x = 14,400
Therefore, the machine can fill 14,400 bottles in 8 hours.
Tatyana can text 225 words in 5 minutes. How many words can Tatyana text in 12 minutes?(1 point)
words
To find out how many words Tatyana can text in 12 minutes, we can use a proportion.
We know that Tatyana can text 225 words in 5 minutes.
Let's set up the proportion:
225 words / 5 minutes = x words / 12 minutes
To solve for x, we can cross multiply:
5 * x = 225 * 12
5x = 2,700
Now, we can divide both sides by 5 to find x:
x = 2,700 / 5
x = 540
Therefore, Tatyana can text 540 words in 12 minutes.
In 4 hours, a comet that is far from the sun usually travels 8,000 miles. How far will the comet travel in 10 hours?(1 point)
miles
To find out how far the comet will travel in 10 hours, we can use a proportion.
We know that in 4 hours, the comet travels 8,000 miles.
Let's set up the proportion:
8,000 miles / 4 hours = x miles / 10 hours
To solve for x, we can cross multiply:
4 * x = 8,000 * 10
4x = 80,000
Now, we can divide both sides by 4 to find x:
x = 80,000 / 4
x = 20,000
Therefore, the comet will travel 20,000 miles in 10 hours.
Question
Brian ran a 5-kilometer race in 40 minutes. How far did he run in 18 minutes? Write your answer as a decimal and do not round.(1 point)
$$
To find out how far Brian ran in 18 minutes, we can set up a proportion using the information given.
We know that Brian ran a 5-kilometer race in 40 minutes.
Let's set up the proportion:
5 kilometers / 40 minutes = x kilometers / 18 minutes
To solve for x, we can cross multiply:
40 * x = 5 * 18
40x = 90
Now, we can divide both sides by 40 to find x:
x = 90 / 40
x = 2.25
Therefore, Brian ran 2.25 kilometers in 18 minutes.
In 3 hours, the Johnson family traveled 195 miles by car. How far will they travel in 5 hours?(1 point)
$$
To find out how far the Johnson family will travel in 5 hours, we can use a proportion.
We know that in 3 hours, the Johnson family traveled 195 miles.
Let's set up the proportion:
195 miles / 3 hours = x miles / 5 hours
To solve for x, we can cross multiply:
3 * x = 195 * 5
3x = 975
Now, we can divide both sides by 3 to find x:
x = 975 / 3
x = 325
Therefore, the Johnson family will travel 325 miles in 5 hours.
To find out how many bottles the machine can fill in 8 hours, we need to use the given information about the machine's filling rate.
Here is the step-by-step explanation:
1. Determine the machine's rate of filling: The machine can fill 5,400 bottles in 3 hours. To find the rate of filling per hour, divide the total number of bottles by the total time taken: 5,400 bottles ÷ 3 hours = 1,800 bottles per hour.
2. Calculate the number of bottles the machine can fill in 8 hours: To find this, we need to multiply the machine's filling rate per hour by the number of hours: 1,800 bottles per hour × 8 hours = 14,400 bottles.
Therefore, the machine can fill 14,400 bottles in 8 hours.