Question

Traveling Sand A sand dune can travel up to $30\mathrm{m}$ per year. How far does the sand dune move per day?

Short answer

The sand dune moves approximately 0.0822 meters per day.

Step-by-step solution

Convert Annual Movement to Daily Movement

To determine how far the sand dune travels in a day, start by dividing the annual movement by the number of days in a year. This calculation assumes that the movement is consistent across all days of the year.

Use the Formula for Daily Movement

The formula to use is: $$\text{Daily Movement}=\frac{\text{Annual Movement}}{\text{Number of Days in a Year}}$$Substitute the given values to get:$$\text{Daily Movement}=\frac{30\mathrm{m}}{365\mathrm{days}}$$

Perform the Calculation

Simplify the fraction from the previous step to find the daily movement. $$\text{Daily Movement}=\frac{30}{365}\mathrm{m}/\mathrm{day}\approx 0.0822\mathrm{m}/\mathrm{day}$$

Key concepts

Unit Conversion

Unit conversion is vital in mathematics and everyday problem-solving. It means changing a measurement from one unit to another.
Think of it as translating a story from one language to another while keeping the meaning intact.
In this exercise, we needed to convert the sand dune's movement from meters per year to meters per day. Here is a simple way to handle unit conversion:

• Identify the starting unit and the desired final unit. In this case, it's from 'year' to 'day.'
• Determine the conversion factor between these units. Here, there are 365 days in a year.
• Multiply or divide your original measurement by this conversion factor.

The key to unit conversion is ensuring you adjust the magnitude without altering the quantity's value.
This adjustment keeps the information consistent across different units of measurement.

Rate Calculation

Calculating rates is about finding out how much one quantity changes with respect to another.
In the context of this exercise, it means determining how far a sand dune moves each day.
We look at finding the rate with these steps:

• Start with a total quantity, like the 30 meters per year in our example.
• Divide this total amount by the time unit you want to measure in, like 365 days for a year.
• The result gives the rate of change, which here is the sand dune's daily movement.

Understanding rate calculation helps us analyze situations better, such as how fast or slow changes happen.
It also applies across many fields, like physics, economics, and everyday life, ensuring precise planning and efficient resource use.

Problem-Solving Steps

Problem-solving in mathematics requires a strategic approach.
It involves clear steps that help break down complex problems into manageable parts.
The essential problem-solving steps include:

• **Understand the problem:** Know what is being asked. Here, it's finding out the daily movement of the sand dune.
• **Plan your approach:** Decide how to solve it. In our exercise, this involved unit conversion and rate calculation.
• **Execute the plan:** Perform calculations following the formula and substitutions.
• **Verify the solution:** Check calculations to ensure accuracy. For example, confirming the division correctness in our daily movement calculation.

These steps form the foundation for solving a variety of mathematical problems, encouraging clarity and confidence regardless of complexity.
By embracing structured approaches, you reduce errors and enhance the problem-solving efficiency.