# Rates in Geology

## Practice problems

Practice calculating rates (and rearranging the rate equation) below using the "rules" that you have just learned. Answers are provided (but try doing them on your own before peeking!).

## Calculating rates

**Problem 1:** You wake up at 6 am (EARLY!) and the temperature is 55°F. By the time you head off to your picnic lunch at noon, the temperature has risen to 91°F. What is the rate of temperature change in °F per hour?

**Problem 2.**The Hawaiian hot spot sits below the Pacific plate. As the plate moves over the hot spot, a chain of volcanoes is formed. The Waianae volcano on Oahu is 3.7 million years old and about 375 km from the current location of the Hawaiian hot spot. Assuming that the hot spot is in a fixed location, how fast (at what rate) is the Pacific plate moving?

**Problem 3:**The Hawaiian hot spot has produced about 775,000,000 km^{3} of magma in the past 70 million years. What is the average rate of magma production per year?

**Problem 4**: Rivers often form sinuous paths as they flow downstream. The river bends are called meanders and move over time as the river erodes its banks. In 2010, you purchased a house that was 150 meters from the outside of a meander of the Rio Grande river. Looking at maps from 1955, you find that the meander has moved 230 meters toward you. How fast is the meander migrating?

Determining a rate from a graph

**Problem 5:** Examine the graph of the age and distance of the New England Seamounts.

This chain of seamounts is thought to be created by a hotspot that underlies the oceanic plate that the seamounts sit on. As the plate moves, it carries the seamounts with it. What is the rate of movement that they show? (You can click on the graph for a bigger version) To solve this problem, first pick any two points on the line and then determine the slope of the line, which is the rate.

If you still need help, you can go back to the explanation page or look at some of the links below.

## Still need more practice?

There are many web sites and books that walk you through the rates problems, although most will be distance, velocity and time problems. However, the mathematics is identical.

**Math.com**has some pages to take you through distance, rate, time questions step-by-step in the ratios and proportions section.**The "Ask Dr. Math" section at mathforum.com**has a relatively clear explanation of distance, rate, time problems in a non-geology setting, as well as about a dozen solved problems at the bottom of the page.**PurpleMath**has some pages to help you solve distance word problems..