Problem 29 - Algebra 2 and Trigonometry

Question

On Monday, Enid spent 45 minutes doing homework. On the remaining four days of the school week spent 15 minutes longer doing homework than she had the day before. Find the total number of minutes Enid spent doing homework from Monday to Friday.

Step-by-Step Solution

Answer

Enid spent 375 minutes doing homework from Monday to Friday.

Step 1: Calculate Tuesday's Homework Time

On Monday, Enid spent 45 minutes doing homework. On Tuesday, she spent 15 minutes more than Monday.Tuesday: \(45 + 15 = 60\) minutes.

Step 2: Calculate Wednesday's Homework Time

Each day, Enid spends 15 minutes more doing homework than the previous day. Therefore, on Wednesday, she will spend 15 minutes more than Tuesday.Wednesday: \(60 + 15 = 75\) minutes.

Step 3: Calculate Thursday's Homework Time

Continuing the pattern, on Thursday, Enid spends 15 minutes more than she did on Wednesday.Thursday: \(75 + 15 = 90\) minutes.

Step 4: Calculate Friday's Homework Time

Following the same pattern, on Friday, Enid spends 15 minutes more than she did on Thursday.Friday: \(90 + 15 = 105\) minutes.

Step 5: Calculate Total Homework Time for the Week

Now, add up the homework times from all five days to find the total.Total Homework Time = Monday + Tuesday + Wednesday + Thursday + FridayTotal: \(45 + 60 + 75 + 90 + 105 = 375\) minutes.

Key Concepts

Understanding Time Calculations

Time calculations are crucial for managing our schedules efficiently. Knowing how to calculate time can help us plan our days better. In the context of Enid's homework problem, time calculations help us figure out how much time she spends in total over several days.
To calculate the total time Enid spent on homework throughout the week, we need to add the number of minutes she spent each day. Starting with the information we have for Monday, we simply add the homework time for each subsequent day to reach the total weekly homework time.
Accurately managing time not only helps in homework calculations but also in various day-to-day activities, like cooking or scheduling appointments. Therefore, practicing time calculations can be quite beneficial in developing time management skills.

The Role of Addition

Addition is one of the fundamental mathematical operations and understanding it thoroughly is essential. In the exercise with Enid, addition allows us to combine the number of minutes she spends each day to calculate the total time.
This fundamental operation involves combining several values into a single sum, and when the values represent time, like in Enid’s scenario, it becomes a practical skill for everyday life. For example:

• On Monday, Enid spends 45 minutes.
• On Tuesday, we add 15 to 45, giving us 60 minutes.
• This process repeats, always adding 15 minutes to the previous day's total.

By performing these additions, we can keep track of Enid's progress, visualize the increase, and ultimately provide a clearer understanding of how small, daily increments accumulate into a larger total.

Recognizing Patterns

Patterns are a regular arrangement or a usual manner of operation that can be identified in numbers, shapes, or even behaviors. Recognizing and understanding patterns can make problem-solving much easier.
In the case of Enid's homework time, there’s a clear pattern. Each day she increases her homework time by 15 minutes from the previous day.

• Monday: 45 minutes
• Tuesday: 60 minutes
• Wednesday: 75 minutes
• Thursday: 90 minutes
• Friday: 105 minutes

See how the number increases by 15 each day? This pattern helps us predict future times and calculate totals quickly.
Understanding this additive sequence not only aids in solving such arithmetic problems but also prepares us to recognize patterns in more complex mathematical concepts, enhancing our analytical skills.