further practice
2. a computer printer can print 480 pages in 15 minutes. what is its printing rate in pages per minute?
3. in 1 minute a traffic light flashes 45 times. how many times will it flash in half an hour?
4. mrs. thomas paid $286 at a paint store for paint that costs $26 a gallon. how many gallons of paint did she buy?
5. a lighthouse flashes its beacon light at a rate of 48 flashes per minute. how many times will the light flash in 30 minutes?
6. an automobile factory can make 18 cars in 8 hours. at this rate, how many cars can the factory assemble in 14 hours?

Question

Accepted Answer

### Question 2
# Explanation:
## Step1: Identify the formula for rate
The printing rate (pages per minute) is calculated by dividing the total number of pages by the total time in minutes. So the formula is $ \text{Rate} = \frac{\text{Total Pages}}{\text{Total Time}} $.
## Step2: Substitute the values
We know the total pages are 480 and the total time is 15 minutes. Substituting these values into the formula, we get $ \text{Rate} = \frac{480}{15} $.
## Step3: Calculate the result
Dividing 480 by 15, we have $ \frac{480}{15} = 32 $.
# Answer:
The printing rate is 32 pages per minute.

### Question 3
# Explanation:
## Step1: Convert half an hour to minutes
Half an hour is 30 minutes (since 1 hour = 60 minutes, so $ \frac{60}{2}=30 $ minutes).
## Step2: Use the rate to find total flashes
The traffic light flashes 45 times per minute. To find the number of flashes in 30 minutes, we multiply the rate (45 flashes per minute) by the time (30 minutes). So the formula is $ \text{Total Flashes} = \text{Rate} \times \text{Time} $, which gives $ 45\times30 $.
## Step3: Calculate the result
Calculating $ 45\times30 = 1350 $.
# Answer:
The traffic light will flash 1350 times in half an hour.

### Question 4
# Explanation:
## Step1: Identify the formula for quantity
The quantity of paint (in gallons) is calculated by dividing the total cost by the cost per gallon. The formula is $ \text{Quantity} = \frac{\text{Total Cost}}{\text{Cost per Gallon}} $.
## Step2: Substitute the values
The total cost is $286 and the cost per gallon is $26. Substituting these values, we get $ \text{Quantity} = \frac{286}{26} $.
## Step3: Calculate the result
Dividing 286 by 26, we have $ \frac{286}{26}=11 $.
# Answer:
Mrs. Thomas bought 11 gallons of paint.

### Question 5
# Explanation:
## Step1: Identify the formula for total flashes
The total number of flashes is calculated by multiplying the rate (flashes per minute) by the time (in minutes). The formula is $ \text{Total Flashes} = \text{Rate} \times \text{Time} $.
## Step2: Substitute the values
The rate is 48 flashes per minute and the time is 30 minutes. Substituting these values, we get $ \text{Total Flashes} = 48\times30 $.
## Step3: Calculate the result
Calculating $ 48\times30 = 1440 $.
# Answer:
The lighthouse beacon will flash 1440 times in 30 minutes.

### Question 6
# Explanation:
## Step1: Find the rate of car production per hour
First, we find out how many cars the factory makes per hour. The factory makes 18 cars in 8 hours. So the rate (cars per hour) is $ \text{Rate} = \frac{\text{Total Cars}}{\text{Total Time}}=\frac{18}{8}=\frac{9}{4} $ cars per hour.
## Step2: Calculate the number of cars in 14 hours
To find the number of cars in 14 hours, we multiply the rate ($ \frac{9}{4} $ cars per hour) by the time (14 hours). So the formula is $ \text{Total Cars} = \text{Rate} \times \text{Time}=\frac{9}{4}\times14 $.
## Step3: Simplify the calculation
$ \frac{9}{4}\times14=\frac{9\times14}{4}=\frac{126}{4} = 31.5 $? Wait, no, wait. Wait, 18 cars in 8 hours, so per hour is $ \frac{18}{8}=2.25 $ cars per hour. Then in 14 hours, it's $ 2.25\times14 $. Let's recalculate:
Wait, maybe a better way: The ratio of time is $ \frac{14}{8} $, so the number of cars is $ 18\times\frac{14}{8} $. Simplify $ \frac{14}{8}=\frac{7}{4} $, so $ 18\times\frac{7}{4}=\frac{126}{4} = 31.5 $? No, that can't be right. Wait, no, 18 cars in 8 hours, so the rate is $ \frac{18}{8}=2.25 $ cars per hour. Then 2.25 * 14: 2*14 =28, 0.25*14 = 3.5, so 28 + 3.5 = 31.5? But cars should be whole numbers? Wait, maybe I made a mistake. Wait, 18 cars in 8 hours, so per hour is 18/8 = 2.25. Then in 14 hours, 2.25*14 = 31.5. But maybe the problem assumes that we can have a fraction? Or maybe I misread the problem. Wait, the problem says "An automobile factory can make 18 cars in 8 hours. At this rate, how many cars can the factory assemble in 14 hours?" So 18 cars in 8 hours, so the rate is 18/8 = 9/4 cars per hour. Then 9/4 *14 = (9*14)/4 = 126/4 = 31.5. But maybe the problem has a typo, or maybe I did wrong. Wait, no, 8 hours:18 cars, 1 hour: 18/8 = 2.25, 14 hours: 2.25*14 = 31.5. So the answer is 31.5? But that's a decimal. Wait, maybe the problem is 18 cars in 6 hours? No, the problem says 8 hours. So according to the calculation, it's 31.5. But let's check again:

Wait, 18 divided by 8 is 2.25. 2.25 times 14: 14*2 =28, 14*0.25=3.5, 28+3.5=31.5. So the factory can assemble 31.5 cars? But that's odd. Maybe the problem is 16 cars in 8 hours? No, the problem says 18. So we have to go with the calculation.

Wait, maybe I made a mistake in step 1. Let's re - do:

Step 1: Find the number of cars per hour. 18 cars in 8 hours, so cars per hour = 18/8 = 2.25.

Step 2: Number of cars in 14 hours = 2.25 *14 = 31.5.

So the answer is 31.5 cars. But since cars are usually whole numbers, maybe there is a mistake in the problem, but according to the given numbers, it's 31.5.

Wait, no, wait, 18 cars in 8 hours, so the rate is 18/8 = 9/4. Then 9/4 *14 = (9*14)/4 = 126/4 = 31.5. So the answer is 31.5.

# Explanation (revised):
## Step1: Determine the production rate per hour
The factory produces 18 cars in 8 hours. The production rate per hour is calculated as $ \text{Rate}=\frac{18}{8} = 2.25 $ cars per hour.
## Step2: Calculate the number of cars in 14 hours
To find the number of cars produced in 14 hours, we multiply the rate (2.25 cars per hour) by the time (14 hours). Using the formula $ \text{Total Cars}=\text{Rate}\times\text{Time} $, we get $ 2.25\times14 $.
## Step3: Compute the result
$ 2.25\times14=(2 + 0.25)\times14=2\times14+0.25\times14 = 28+3.5 = 31.5 $.
# Answer:
The factory can assemble 31.5 cars in 14 hours. (If we assume that partial cars are not considered, there might be an error in the problem's numbers, but based on the given data, this is the result.)

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QUESTION IMAGE

Question

Explanation:

Question 2

Step1: Identify the formula for rate

Step2: Substitute the values

Step3: Calculate the result

Step1: Convert half an hour to minutes

Step2: Use the rate to find total flashes

Step3: Calculate the result

Step1: Identify the formula for quantity

Step2: Substitute the values

Step3: Calculate the result

Answer:

Question 3