Problem 34 - Algebra 2

Question

Geologists estimate that the continents of Europe and North America are drifting apart at a rate of an average of 12 miles every 1 million years, or about 0.75 inch per year. If the continents continue to drift apart at that rate, how many inches will they drift in 50 years? (Hint: \(a_{1}=0.75\))

Step-by-Step Solution

Answer

The continents will drift 37.5 inches in 50 years.

Step 1: Understanding the Problem

We need to calculate the total drift distance of the continents in inches over a span of 50 years, given that the annual drift rate is 0.75 inches.

Step 2: Formulate the Calculation

Given that the drift rate is constant at 0.75 inches per year, we multiply this rate by the number of years (50 years) to find the total drift distance.

Step 3: Perform the Calculation

Calculate the total drift by multiplying the annual drift rate (0.75 inches/year) by the number of years (50):\[\text{Total Drift} = 0.75 \times 50\]

Step 4: Final Calculation

\[\text{Total Drift} = 37.5\] inches. Hence, the continents will drift apart by 37.5 inches in 50 years.

Key Concepts

Geologic Drift

Geologic drift is a fascinating natural process that describes the movement of continents over geological time scales. To better grasp this concept, imagine our planet as a gigantic jigsaw puzzle where each piece represents a continent. These continental pieces are not stationary; they are continuously shifting or drifting, albeit extremely slowly. The movement is caused by tectonic activity beneath the Earth's crust. These activities are driven by forces such as mantle convection, slab pull, and ridge push.

In the specific case of Europe and North America, they are moving away from each other at an average rate of 12 miles every 1 million years, which breaks down to roughly 0.75 inches per year. Though it seems insignificant in the short term, over millions of years, this drift significantly reshapes the face of our planet, influencing everything from climate patterns to the course of ocean currents.

Distance Calculation

When calculating distance, especially over long periods, it's crucial to accurately grasp the rate at which an event occurs and apply it consistently over time. In our exercise example, we need to calculate how far apart the continents will drift in 50 years, given a constant annual drift rate of 0.75 inches.

This calculation is straightforward: we multiply the annual drift rate by the number of years to find the total drift. Mathematically, this can be represented as:

• Drift Rate: 0.75 inches/year
• Time Span: 50 years

Thus, the formula to find the drift over 50 years becomes:

• \[\text{Total Drift} = \text{Drift Rate} \times \text{Time Span} = 0.75 \times 50\]
• The solution gives us 37.5 inches).

This simple multiplication provides insight into how far the continents have moved over five decades. This concept is not limited to geology; similar calculations are often used in various fields, whenever it's necessary to project movement or change over time.

Unit Conversion

Unit conversion is an essential skill in science and everyday life, enabling you to understand and compare different quantities. In our example, we are dealing with the conversion of the rate of continental drift. The original information was provided in miles per million years and has been converted to inches per year.

Understanding how to convert between units is crucial. Here's a quick reminder of the conversion related to our problem:

• 1 mile equals 63,360 inches. Since the drift is 12 miles per 1 million years, convert it to inches:
• \[12 \text{ miles} \times 63,360 \text{ inches/mile} = 760,320 \text{ inches}\]
• To find the drift per year, divide by 1,000,000 years:\[\frac{760,320 \text{ inches}}{1,000,000 \text{ years}} \approx 0.76 \text{ inches/year}\]

This conversion helps clarify rates of drift in more manageable terms for smaller timeframes, like years, enabling us to see how much these enormous geological forces affect our planet on a human timescale.