Solved on Jan 28, 2024

Niimi reads 23 pages in 30 minutes. How long would it take her to read a 100-page book? Set up a proportion, show work, and express the answer in hours and minutes.
Solution: Let $x$ be the time (in minutes) it takes Niimi to read the 100-page book. Then, $\frac{23}{30} = \frac{100}{x}$ . Solving for $x$ , we get $x = \frac{100 \times 30}{23} = 130$ minutes. This is equivalent to 2 hours and 10 minutes.

STEP 1

Assumptions
1. Niimi can read 23 pages in 30 minutes.
2. The book has 100 pages.
3. We need to find the time it takes to read the entire book in hours and minutes.
4. We will use a proportion to solve the problem.
5. If necessary, we will round the time to the nearest minute.

STEP 2

Set up a proportion to relate the number of pages Niimi can read to the time it takes. We have two ratios: the known rate of reading (23 pages per 30 minutes) and the unknown rate (100 pages per x minutes).
$\frac{23 \text{ pages}}{30 \text{ minutes}} = \frac{100 \text{ pages}}{x \text{ minutes}}$

STEP 3

Cross-multiply to solve for $x$ , the number of minutes it takes to read 100 pages.
$23x = 100 \times 30$

STEP 4

Calculate the product on the right side of the equation.
$23x = 3000$

STEP 5

Divide both sides of the equation by 23 to solve for $x$ .
$x = \frac{3000}{23}$

STEP 6

Calculate the value of $x$ .
$x \approx 130.43 \text{ minutes}$

STEP 7

Since we want the time in hours and minutes, we need to convert 130.43 minutes to hours and the remaining minutes. There are 60 minutes in an hour.
$\text{Hours} = \frac{130.43 \text{ minutes}}{60}$

STEP 8

Calculate the number of hours.
$\text{Hours} \approx 2.1738$

STEP 9

Since we only need the whole number of hours, we take the integer part of 2.1738, which is 2 hours.
$\text{Whole hours} = 2 \text{ hours}$

STEP 10

To find the remaining minutes, we take the decimal part of 2.1738 and multiply it back by 60.
$\text{Remaining minutes} = 0.1738 \times 60$

STEP 11

Calculate the remaining minutes.
$\text{Remaining minutes} \approx 10.428 \text{ minutes}$

STEP 12

Round the remaining minutes to the nearest minute.
$\text{Rounded minutes} = 10 \text{ minutes}$

STEP 13

Combine the hours and minutes to express the total time it takes Niimi to read the 100-page book.
$\text{Total time} = 2 \text{ hours and } 10 \text{ minutes}$

STEP 14

Write a concluding statement.
Niimi can read a 100-page book in approximately 2 hours and 10 minutes.

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STEP 1

Assumptions
1. Niimi can read 23 pages in 30 minutes.
2. The book has 100 pages.
3. We need to find the time it takes to read the entire book in hours and minutes.
4. We will use a proportion to solve the problem.
5. If necessary, we will round the time to the nearest minute.

STEP 2

Set up a proportion to relate the number of pages Niimi can read to the time it takes. We have two ratios: the known rate of reading (23 pages per 30 minutes) and the unknown rate (100 pages per x minutes).
$\frac{23 \text{ pages}}{30 \text{ minutes}} = \frac{100 \text{ pages}}{x \text{ minutes}}$

STEP 3

Cross-multiply to solve for $x$ , the number of minutes it takes to read 100 pages.
$23x = 100 \times 30$

STEP 4

Calculate the product on the right side of the equation.
$23x = 3000$

STEP 5

Divide both sides of the equation by 23 to solve for $x$ .
$x = \frac{3000}{23}$

STEP 6

Calculate the value of $x$ .
$x \approx 130.43 \text{ minutes}$

STEP 7

Since we want the time in hours and minutes, we need to convert 130.43 minutes to hours and the remaining minutes. There are 60 minutes in an hour.
$\text{Hours} = \frac{130.43 \text{ minutes}}{60}$

STEP 8

Calculate the number of hours.
$\text{Hours} \approx 2.1738$

STEP 9

Since we only need the whole number of hours, we take the integer part of 2.1738, which is 2 hours.
$\text{Whole hours} = 2 \text{ hours}$

STEP 10

To find the remaining minutes, we take the decimal part of 2.1738 and multiply it back by 60.
$\text{Remaining minutes} = 0.1738 \times 60$

STEP 11

Calculate the remaining minutes.
$\text{Remaining minutes} \approx 10.428 \text{ minutes}$

STEP 12

Round the remaining minutes to the nearest minute.
$\text{Rounded minutes} = 10 \text{ minutes}$

STEP 13

Combine the hours and minutes to express the total time it takes Niimi to read the 100-page book.
$\text{Total time} = 2 \text{ hours and } 10 \text{ minutes}$

STEP 14

Write a concluding statement.
Niimi can read a 100-page book in approximately 2 hours and 10 minutes.

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STEP 1

Assumptions1. Niimi can read 23 pages in 30 minutes.2. The book has 100 pages.3. We need to find the time it takes to read the entire book in hours and minutes.4. We will use a proportion to solve the problem.5. If necessary, we will round the time to the nearest minute.

STEP 2

STEP 3

Cross-multiply to solve for x x x, the number of minutes it takes to read 100 pages.23x=100×3023x = 100 \times 3023x=100×30

STEP 4

Calculate the product on the right side of the equation.23x=300023x = 300023x=3000

STEP 5

Divide both sides of the equation by 23 to solve for x x x.x=300023x = \frac{3000}{23}x=233000​

STEP 6

Calculate the value of x x x.x≈130.43 minutesx \approx 130.43 \text{ minutes}x≈130.43 minutes

STEP 7

Since we want the time in hours and minutes, we need to convert 130.43 minutes to hours and the remaining minutes. There are 60 minutes in an hour.Hours=130.43 minutes60\text{Hours} = \frac{130.43 \text{ minutes}}{60}Hours=60130.43 minutes​

STEP 8

Calculate the number of hours.Hours≈2.1738\text{Hours} \approx 2.1738Hours≈2.1738

STEP 9

Since we only need the whole number of hours, we take the integer part of 2.1738, which is 2 hours.Whole hours=2 hours\text{Whole hours} = 2 \text{ hours}Whole hours=2 hours

STEP 10

To find the remaining minutes, we take the decimal part of 2.1738 and multiply it back by 60.Remaining minutes=0.1738×60\text{Remaining minutes} = 0.1738 \times 60Remaining minutes=0.1738×60

STEP 11

Calculate the remaining minutes.Remaining minutes≈10.428 minutes\text{Remaining minutes} \approx 10.428 \text{ minutes}Remaining minutes≈10.428 minutes

STEP 12

Round the remaining minutes to the nearest minute.Rounded minutes=10 minutes\text{Rounded minutes} = 10 \text{ minutes}Rounded minutes=10 minutes

STEP 13

Combine the hours and minutes to express the total time it takes Niimi to read the 100-page book.Total time=2 hours and 10 minutes\text{Total time} = 2 \text{ hours and } 10 \text{ minutes}Total time=2 hours and 10 minutes

STEP 14

Write a concluding statement.Niimi can read a 100-page book in approximately 2 hours and 10 minutes.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Assumptions
1. Niimi can read 23 pages in 30 minutes.
2. The book has 100 pages.
3. We need to find the time it takes to read the entire book in hours and minutes.
4. We will use a proportion to solve the problem.
5. If necessary, we will round the time to the nearest minute.

Cross-multiply to solve for $x$ , the number of minutes it takes to read 100 pages.
$23x = 100 \times 30$

Calculate the product on the right side of the equation.
$23x = 3000$

Divide both sides of the equation by 23 to solve for $x$ .
$x = \frac{3000}{23}$

Calculate the value of $x$ .
$x \approx 130.43 \text{ minutes}$

Since we want the time in hours and minutes, we need to convert 130.43 minutes to hours and the remaining minutes. There are 60 minutes in an hour.
$\text{Hours} = \frac{130.43 \text{ minutes}}{60}$

Calculate the number of hours.
$\text{Hours} \approx 2.1738$

Since we only need the whole number of hours, we take the integer part of 2.1738, which is 2 hours.
$\text{Whole hours} = 2 \text{ hours}$

To find the remaining minutes, we take the decimal part of 2.1738 and multiply it back by 60.
$\text{Remaining minutes} = 0.1738 \times 60$

Calculate the remaining minutes.
$\text{Remaining minutes} \approx 10.428 \text{ minutes}$

Round the remaining minutes to the nearest minute.
$\text{Rounded minutes} = 10 \text{ minutes}$

Combine the hours and minutes to express the total time it takes Niimi to read the 100-page book.
$\text{Total time} = 2 \text{ hours and } 10 \text{ minutes}$

Write a concluding statement.
Niimi can read a 100-page book in approximately 2 hours and 10 minutes.