Question

If \(10 \mathrm{~km}\) of seafloor were created in 50,000 years, how many kilometers of seafloor were created in 10,000 years? How many years will it take to create a total of \(30 \mathrm{~km}\) of seafloor?

Short answer

In 10,000 years, 2 km of seafloor are created. It takes 150,000 years to create 30 km.

Step-by-step solution

Understand the Rate of Seafloor Creation

The problem states that 10 km of seafloor were created in 50,000 years. To find the rate, divide the distance by the time: \( \text{Rate} = \frac{10 \text{ km}}{50,000 \text{ years}} = 0.0002 \text{ km/year} \). This is the rate of seafloor creation.

Calculate Kilometers Created in 10,000 Years

With the rate of seafloor creation known, determine how many kilometers are made in 10,000 years by multiplying the rate by the time: \( \text{Distance} = 0.0002 \text{ km/year} \times 10,000 \text{ years} = 2 \text{ km} \).

Calculate Years Required for 30 km Seafloor

To find how long it takes to create 30 km of seafloor, rearrange the rate formula to solve for time: \( \text{Time} = \frac{\text{Distance}}{\text{Rate}} = \frac{30 \text{ km}}{0.0002 \text{ km/year}} = 150,000 \text{ years} \).

Key concepts

Rate of Seafloor Creation

Seafloor spreading is a geological process where new oceanic crust is formed at mid-ocean ridges. It is a fascinating process that helps scientists understand plate tectonics and the dynamics of Earth's crust. But how do we quantify this seafloor creation?
One key aspect is determining the rate at which new seafloor is formed. To calculate it, we use the formula:

• Rate = \(\frac{\text{Distance}}{\text{Time}}\)

In the given exercise, 10 kilometers (km) of seafloor were formed over 50,000 years. Dividing the distance by the time gives us a rate of creation:

• \(\text{Rate} = \frac{10 \text{ km}}{50,000 \text{ years}}\)
• \(\text{Rate} = 0.0002 \text{ km/year}\)

This means for every year, 0.0002 kilometers of seafloor are created. Understanding this rate helps us predict how much new seafloor is formed over varying periods.

Kilometer per Year Calculations

Once the rate of seafloor creation is known, we can use it to determine distances formed over time. It is simply a matter of multiplying the rate by the number of years. This exercise demonstrates the calculation for 10,000 years:

• Distance = Rate x Time
• \(\text{Distance} = 0.0002 \text{ km/year} \times 10,000 \text{ years}\)
• \(\text{Distance} = 2 \text{ km}\)

This result indicates that in 10,000 years, 2 kilometers of new seafloor will be created.
Such calculations are straightforward but crucial when determining the extent of geological activities over given periods. They provide insight into how much seafloor can be expected from a given time frame, based on the fixed rate of spreading.

Time and Distance Problem Solving

Sometimes, we might need to find out how long it will take for a particular amount of seafloor to form, given a known rate. This involves rearranging the rate formula to solve for time:

• Time = \(\frac{\text{Distance}}{\text{Rate}}\)

In this scenario, if we need to know how many years it would take to form 30 km of seafloor:

• Time = \(\frac{30 \text{ km}}{0.0002 \text{ km/year}}\)
• Time = 150,000 years

This calculation is insightful for understanding the temporal scale of seafloor creation.
It shows that significant geological formations, like creating a substantial amount of seafloor, require extensive time. Conceptually, this underscores the slow yet continuous nature of geological processes shaping our planet.