Question

Quantity \(\underline{A}\) The number of seconds in 7 hours Quantity \(\mathrm{B}\) The number of hours in 52 weeks A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given.

Short answer

B. Quantity B is greater.

Step-by-step solution

Understanding Quantity A

Quantity A represents the total number of seconds in 7 hours. To find this, convert hours to minutes and then to seconds. There are 60 minutes in one hour and 60 seconds in one minute. Therefore, the number of seconds in 7 hours can be found using the formula: \[ 7 \text{ hours} \times 60 \text{ minutes/hour} \times 60 \text{ seconds/minute} \]

Calculate Quantity A

Perform the multiplication to convert 7 hours into seconds: \[ 7 \times 60 \times 60 = 25200 \text{ seconds} \] Hence, Quantity A is 25200 seconds.

Understanding Quantity B

Quantity B represents the total number of hours in 52 weeks. To calculate this, convert weeks into days and days into hours. There are 7 days in one week and 24 hours in one day. Therefore, the number of hours in 52 weeks is: \[ 52 \text{ weeks} \times 7 \text{ days/week} \times 24 \text{ hours/day} \]

Calculate Quantity B

Perform the multiplication to find the total number of hours in 52 weeks: \[ 52 \times 7 \times 24 = 8736 \text{ hours} \] Hence, Quantity B is 8736 hours.

Compare Quantities A and B

Now compare the two quantities: Quantity A is 25200 seconds. Quantity B is 8736 hours. Since 1 hour = 3600 seconds, convert Quantity B to seconds for a fair comparison: \[ 8736 \text{ hours} \times 3600 \text{ seconds/hour} = 31449600 \text{ seconds} \] Hence, Quantity B in seconds is much larger than Quantity A.

Key concepts

Unit Conversions

Unit conversions are essential in solving many quantitative problems. They allow us to express a quantity in different units of measurement. In this exercise, the conversions between hours to minutes, minutes to seconds, weeks to days, and days to hours are crucial.

The basic unit conversions used in this problem are:

• 1 hour = 60 minutes
• 1 minute = 60 seconds
• 1 week = 7 days
• 1 day = 24 hours

By applying these conversions, we can interchange between different time units. For instance, to convert 7 hours into seconds, you first convert hours to minutes (7 hours * 60 minutes/hour) and then convert those minutes to seconds (420 minutes * 60 seconds/minute). The final result is 25200 seconds.

Basic Arithmetic

Basic arithmetic involves simple mathematical operations like addition, subtraction, multiplication, and division. In this problem, multiplication is predominantly used to convert units. For example, to determine the total hours in 52 weeks, consider the conversion sequence:

• 52 weeks * 7 days/week = 364 days
• 364 days * 24 hours/day = 8736 hours

The multiplication steps systematically break down the problem into manageable parts. Each step provides a clear pathway to the final answer by applying basic arithmetic rules.

Time Measurement

Understanding time measurement is vital in solving this exercise. This concept includes the knowledge of how time units relate to each other. Time is generally measured in seconds, minutes, hours, days, weeks, months, and years. The problem explores the relationships between hours and seconds, and between weeks and hours.

To illustrate:

• Seconds in 7 hours: Multiply hours by 60 to get minutes, then multiply minutes by 60 to get seconds.
• Hours in 52 weeks: Multiply weeks by 7 to get days, then multiply days by 24 to get hours.

Here, recognizing these relationships helps in accurately converting and comparing time units. Once you grasp these conversions, comparing different quantities becomes much simpler.