1. A Single Man Works At A Rate Of $\frac{5}{3}$ Tasks Per Hour. $\[ \text{Time} = \frac{20}{\frac{5}{3}} = 12 \text{ Hours} \\]2. The Ratio Of Boys To Girls In Grade 9 Is $7:5$. How Many More Boys Than Girls Are In

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1.1 Understanding the Problem

Calculating Time to Complete Tasks

When a single man works at a rate of $\frac{5}{3}$ tasks per hour, it means he can complete $\frac{5}{3}$ tasks in one hour. To find the time it takes to complete a certain number of tasks, we can use the formula:

Time = Total Tasks / Rate

In this case, the total tasks is 20, and the rate is $\frac{5}{3}$ tasks per hour.

1.2 Calculating Time

To calculate the time it takes to complete 20 tasks, we can plug in the values into the formula:

Time = 20 / $\frac{5}{3}$

To divide by a fraction, we can multiply by its reciprocal:

Time = 20 * $\frac{3}{5}$

Time = $\frac{20 * 3}{5}$

Time = $\frac{60}{5}$

Time = 12 hours

Therefore, it will take the single man 12 hours to complete 20 tasks at a rate of $\frac{5}{3}$ tasks per hour.

1.3 Conclusion

In conclusion, when a single man works at a rate of $\frac{5}{3}$ tasks per hour, it will take him 12 hours to complete 20 tasks.

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2.1 Understanding the Problem

Calculating the Difference in Number of Boys and Girls

The ratio of boys to girls in Grade 9 is $7:5$, which means that for every 7 boys, there are 5 girls. To find the difference in the number of boys and girls, we need to find the total number of boys and girls.

2.2 Calculating the Total Number of Boys and Girls

Let's assume that the total number of boys and girls is 12x, where x is a positive integer. We can set up the following equation:

7x + 5x = 12x

Combine like terms:

12x = 12x

This equation is true for any value of x. Therefore, we can choose any value of x to find the total number of boys and girls.

2.3 Choosing a Value for x

Let's choose x = 1. Then, the total number of boys and girls is:

Total Boys = 7x = 7(1) = 7

Total Girls = 5x = 5(1) = 5

2.4 Calculating the Difference

To find the difference in the number of boys and girls, we can subtract the number of girls from the number of boys:

Difference = Total Boys - Total Girls

Difference = 7 - 5

Difference = 2

Therefore, there are 2 more boys than girls in Grade 9.

2.5 Conclusion

In conclusion, when the ratio of boys to girls in Grade 9 is $7:5$, there are 2 more boys than girls in Grade 9.

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3.1 Understanding the Problem

Calculating Time to Complete Tasks and Difference in Number of Boys and Girls

The problem consists of two parts: calculating the time it takes to complete 20 tasks at a rate of $\frac{5}{3}$ tasks per hour, and finding the difference in the number of boys and girls in Grade 9 when the ratio of boys to girls is $7:5$.

3.2 Calculating Time to Complete Tasks

To calculate the time it takes to complete 20 tasks, we can use the formula:

Time = Total Tasks / Rate

In this case, the total tasks is 20, and the rate is $\frac{5}{3}$ tasks per hour.

3.3 Calculating Time

To calculate the time it takes to complete 20 tasks, we can plug in the values into the formula:

Time = 20 / $\frac{5}{3}$

To divide by a fraction, we can multiply by its reciprocal:

Time = 20 * $\frac{3}{5}$

Time = $\frac{20 * 3}{5}$

Time = $\frac{60}{5}$

Time = 12 hours

Therefore, it will take 12 hours to complete 20 tasks at a rate of $\frac{5}{3}$ tasks per hour.

3.4 Calculating the Difference in Number of Boys and Girls

To find the difference in the number of boys and girls, we can subtract the number of girls from the number of boys:

Difference = Total Boys - Total Girls

Difference = 7 - 5

Difference = 2

Therefore, there are 2 more boys than girls in Grade 9.

3.5 Conclusion

In conclusion, when a single man works at a rate of $\frac{5}{3}$ tasks per hour, it will take him 12 hours to complete 20 tasks. Additionally, when the ratio of boys to girls in Grade 9 is $7:5$, there are 2 more boys than girls in Grade 9.

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In conclusion, the problem consists of two parts: calculating the time it takes to complete 20 tasks at a rate of $\frac{5}{3}$ tasks per hour, and finding the difference in the number of boys and girls in Grade 9 when the ratio of boys to girls is $7:5$. We have calculated that it will take 12 hours to complete 20 tasks at a rate of $\frac{5}{3}$ tasks per hour, and there are 2 more boys than girls in Grade 9.

Q1: What is the formula to calculate the time it takes to complete a certain number of tasks at a given rate?

A1: The formula to calculate the time it takes to complete a certain number of tasks at a given rate is:

Time = Total Tasks / Rate

Q2: How do I calculate the time it takes to complete 20 tasks at a rate of $\frac{5}{3}$ tasks per hour?

A2: To calculate the time it takes to complete 20 tasks at a rate of $\frac{5}{3}$ tasks per hour, you can plug in the values into the formula:

Time = 20 / $\frac{5}{3}$

To divide by a fraction, you can multiply by its reciprocal:

Time = 20 * $\frac{3}{5}$

Time = $\frac{20 * 3}{5}$

Time = $\frac{60}{5}$

Time = 12 hours

Q3: What is the ratio of boys to girls in Grade 9?

A3: The ratio of boys to girls in Grade 9 is $7:5$.

Q4: How many more boys than girls are in Grade 9?

A4: To find the difference in the number of boys and girls, you can subtract the number of girls from the number of boys:

Difference = Total Boys - Total Girls

Difference = 7 - 5

Difference = 2

Therefore, there are 2 more boys than girls in Grade 9.

Q5: What is the total number of boys and girls in Grade 9?

A5: Let's assume that the total number of boys and girls is 12x, where x is a positive integer. We can set up the following equation:

7x + 5x = 12x

Combine like terms:

12x = 12x

This equation is true for any value of x. Therefore, we can choose any value of x to find the total number of boys and girls.

Q6: How do I choose a value for x?

A6: You can choose any value of x to find the total number of boys and girls. For example, let's choose x = 1. Then, the total number of boys and girls is:

Total Boys = 7x = 7(1) = 7

Total Girls = 5x = 5(1) = 5

Q7: What is the difference in the number of boys and girls in Grade 9?

A7: The difference in the number of boys and girls in Grade 9 is 2.

Q8: What is the conclusion of the problem?

A8: In conclusion, when a single man works at a rate of $\frac{5}{3}$ tasks per hour, it will take him 12 hours to complete 20 tasks. Additionally, when the ratio of boys to girls in Grade 9 is $7:5$, there are 2 more boys than girls in Grade 9.

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Q1: What is the formula to calculate the time it takes to complete a certain number of tasks at a given rate?

A1: The formula to calculate the time it takes to complete a certain number of tasks at a given rate is:

Time = Total Tasks / Rate

Q2: How do I calculate the time it takes to complete a certain number of tasks at a given rate?

A2: To calculate the time it takes to complete a certain number of tasks at a given rate, you can plug in the values into the formula:

Time = Total Tasks / Rate

Q3: What is the ratio of boys to girls in Grade 9?

A3: The ratio of boys to girls in Grade 9 is $7:5$.

Q4: How many more boys than girls are in Grade 9?

A4: To find the difference in the number of boys and girls, you can subtract the number of girls from the number of boys:

Difference = Total Boys - Total Girls

Difference = 7 - 5

Difference = 2

Therefore, there are 2 more boys than girls in Grade 9.

Q5: What is the total number of boys and girls in Grade 9?

A5: Let's assume that the total number of boys and girls is 12x, where x is a positive integer. We can set up the following equation:

7x + 5x = 12x

Combine like terms:

12x = 12x

This equation is true for any value of x. Therefore, we can choose any value of x to find the total number of boys and girls.

Q6: How do I choose a value for x?

A6: You can choose any value of x to find the total number of boys and girls. For example, let's choose x = 1. Then, the total number of boys and girls is:

Total Boys = 7x = 7(1) = 7

Total Girls = 5x = 5(1) = 5

Q7: What is the difference in the number of boys and girls in Grade 9?

A7: The difference in the number of boys and girls in Grade 9 is 2.

Q8: What is the conclusion of the problem?

A8: In conclusion, when a single man works at a rate of $\frac{5}{3}$ tasks per hour, it will take him 12 hours to complete 20 tasks. Additionally, when the ratio of boys to girls in Grade 9 is $7:5$, there are 2 more boys than girls in Grade 9.