Problem 39 - Prealgebra

Question

Stationary Bike Maggie rides a stationary bike for 1 hour and 15 minutes, 4 days a week. After 2 weeks, how many hours has she spent riding the stationary bike?

Step-by-Step Solution

Answer

Maggie spent 10 hours riding the stationary bike in two weeks.

Step 1: Convert Time to Decimal

First, we need to convert the time Maggie spends biking in hours and minutes into a pure decimal form. She rides for 1 hour and 15 minutes. To convert this to hours, we know that 15 minutes is a quarter of an hour, or \( \frac{15}{60} = 0.25 \) hours. So, 1 hour and 15 minutes is \( 1 + 0.25 = 1.25 \) hours.

Step 2: Calculate Total Weekly Time

Now calculate how much time Maggie spends biking in one week. Since she rides 4 days a week, the total weekly time is \( 4 \times 1.25 \) hours. Performing the multiplication gives: \(4 \times 1.25 = 5 \) hours per week.

Step 3: Calculate Total Time for Two Weeks

Maggie bikes for 2 weeks, so we multiply the weekly time by 2 to find out the total time spent biking in two weeks. \( 5 \times 2 = 10 \) hours.

Key Concepts

Decimal Conversion

When dealing with time, particularly when it combines hours and minutes, it’s useful to convert this into a decimal format. This makes calculations such as multiplication and addition much more straightforward. Let’s illustrate how to perform this conversion using Maggie's biking time. Maggie bikes for 1 hour and 15 minutes each session. The important piece to note is that 15 minutes doesn't directly convert into 0.15 hours. Instead, you need to know the fraction form, because time is typically divided into 60-minute increments.
Here's how to convert minutes into a decimal:

• Start by understanding that there are 60 minutes in an hour.
• Therefore, converting minutes to hours is achieved by dividing the number of minutes by 60.

For 15 minutes, the calculation is \( \frac{15}{60} = 0.25 \) hours. So, 1 hour and 15 minutes convert into \(1 + 0.25 = 1.25\) hours. By converting and working with decimals, it’s much easier to multiply or compare time durations.

Multiplication of Fractions

When calculating how much time Maggie spends each week on her stationary bike, you need to understand how to use multiplication effectively with decimal time values. In this case, 1.25 hours, the decimal conversion of her biking time, needs to be multiplied by the number of days she rides each week to calculate her total weekly biking time.
Here is the importance of multiplication in this calculation:

• Maggie rides her bike 4 days a week.
• Using decimals, multiply the decimal hours 1.25 by 4 days: \( 4 \times 1.25 \).

When you execute the multiplication, you calculate the total time Maggie rides each week. Performing this arithmetic gives a straightforward result of 5 hours per week. It’s vital to be clear with each step to ensure no mistakes, as fractional multiplication will slightly vary from traditional number multiplication due to the decimal places involved.

Time Calculation

Time calculations, especially when determining how many hours are accumulated over multiple sessions, are an essential skill. For Maggie’s biking schedule, this involves multiplying her weekly time commitment over a two-week span.
Here’s how:

• Once the weekly time (5 hours) is calculated, you can multiply this by the number of weeks Maggie continues her routine.
• In this scenario, multiply: \( 5 \times 2 \).

By doing so, you reach a final total of 10 hours spent biking over the two weeks. This step illustrates how repeated activities over a set period can accumulate, and also stresses the importance of understanding simple multiplications with time periods. Being able to break down and calculate accumulated time can help in planning, managing schedules, or even tracking fitness goals effectively.