Last year, Julia had already exercised 35 hours prior to May 1. She then exercised $\frac{1}{2}$ hour per day on some days during the rest of the year. Which of the following equations gives the total amount of hours, $h$, Julia exercised last year if she exercised $d$ days the rest of the year? $(0 \leq d \leq 245)$
h=0.5 d
h=0.5 d+35
h=35 d
h=35 d+0.5
Answer (1)
Julia exercised 35 hours before May 1.
She exercised 2 1 hour per day for d days after May 1, which is 0.5 d hours.
The total hours, h , is the sum of these two: h = 0.5 d + 35 .
Therefore, the equation that gives the total amount of hours Julia exercised last year is h = 0.5 d + 35 .
Explanation
Problem Analysis Let's analyze the problem. Julia exercised 35 hours before May 1. After May 1, she exercised 2 1 hour per day for d days. We need to find the equation that represents the total hours, h , Julia exercised last year.
Hours Exercised After May 1 The total hours Julia exercised after May 1 is the product of the number of days, d , and the hours exercised per day, 2 1 . This can be written as 2 1 d or 0.5 d .
Total Hours Exercised To find the total hours exercised last year, we add the hours exercised before May 1 (35 hours) to the hours exercised after May 1 ( 0.5 d hours). This gives us the equation h = 0.5 d + 35 .
Examples
Imagine you're tracking your study hours. You've already studied 35 hours before the semester officially starts. If you plan to study an additional half-hour each day for the next d days, the equation h = 0.5 d + 35 helps you calculate your total study hours, h , by the end of that period. This kind of calculation is useful for planning and tracking progress towards your academic goals.
