Question

First solve the problem, and then enter your answer on the grid provided on the answer sheet. The instructions for entering your answers follow. Eloise is told by her doctor that she should try to average 9 hours of sleep a night because that is what a typical teenager needs for optimal mental and physical health. If Eloise was awake for 126 hours in a given week, how many additional hours of sleep should she have had in order to follow her doctor's advice?

Short answer

Eloise needs 21 more hours of sleep.

Step-by-step solution

Determine Total Weekly Sleeping Hours Needed

This problem asks us to calculate how much sleep Eloise needs in a week. The doctor advises 9 hours of sleep per night. Therefore, calculate the weekly required sleep: 9 hours/night * 7 nights = 63 total hours of sleep needed per week.

Calculate Total Hours in a Week

There are 7 days in a week, and each day has 24 hours. Therefore, the total number of hours in a week is: 7 days * 24 hours/day = 168 hours.

Calculate the Hours Eloise Slept

We know that Eloise was awake for 126 hours during the week. To find out how much she actually slept, subtract the awake hours from the total hours in the week: 168 hours - 126 hours = 42 hours of sleep.

Calculate Additional Sleep Needed

Now, we compare Eloise's actual sleep hours to the recommended sleep hours (63 hours). Subtract the slept hours from the needed hours to determine the additional sleep needed: 63 hours - 42 hours = 21 more hours of sleep needed.

Key concepts

Time Calculation

Understanding the concept of time calculation is crucial for solving problems involving schedules, planning, and other time-related queries. Time calculation helps us grasp the notion of converting between different time units, such as days, hours, and minutes.
To calculate time effectively, remember that a single day consists of 24 hours. So, when calculating weekly hours, simply multiply the number of days by the number of hours in each day.

• 1 week = 7 days
• 1 day = 24 hours
• Total weekly hours = 7 days * 24 hours/day = 168 hours

A clear understanding of these conversions aids in determining how much time one can allocate to different activities in a week. It helps when comparing how many hours are spent on different tasks, including sleep and work. Using these concepts, you can efficiently calculate time intervals and better manage your schedule.

Sleep Recommendation

Getting enough sleep is vital for maintaining overall health, especially for growing teenagers. Doctors often recommend around 9 hours of sleep each night for adolescents. This recommendation is based on the need for sufficient rest to support mental and physical development during these crucial years.
By following this guideline, teenagers can ensure they are well-rested, which can lead to improved focus, better mood, and enhanced learning capabilities.
In Eloise's case, her doctor advised 9 hours of sleep per night. Therefore, the total weekly sleep required would be:

• 9 hours/night * 7 nights/week = 63 hours of sleep per week

Calculating your own sleep needs similarly can help ensure you get the appropriate rest your body requires. Prioritizing sleep can lead to better health outcomes and improved daily performance.

Basic Arithmetic

Basic arithmetic involves operations like addition, subtraction, multiplication, and division to solve everyday problems. Understanding these arithmetic operations is crucial for tackling a variety of mathematical challenges, including those related to time and lifestyle habits.
In Eloise's situation, mastering basic arithmetic allowed us to determine her sleeping pattern discrepancies. Here's a breakdown of tasks accomplished using basic arithmetic:

• Calculate total hours in the week: 7 days * 24 hours = 168 hours
• Subtract the awake hours from the total weekly hours to find the sleeping hours
• 168 hours (total hours) - 126 hours (awake hours) = 42 sleeping hours
• Compare slept hours against the recommended 63 hours
• 63 hours (recommended sleep) - 42 hours (actual sleep) = 21 additional hours needed

By applying basic arithmetic, we can solve problems efficiently, making it easier to follow recommendations and manage our time and health effectively. Always double-check your calculations to ensure accuracy.