The word rate can be defined as the amount that something measurable -- such as money, temperature or distance -- changes over time. Speed is the rate at which distance changes over time. Students in math and physical science classes are often asked to solve rate problems, the first of which usually deal with speed. Problems may involve calculating speed itself or rearranging the equation for speed to solve for time or distance.
The Equation for Rate
All rates have equations associated with them. The equations relate the change being measured and the amount of time that has passed. The equation for speed is the rate equation that relates distance and time. Speed is mathematically defined as distance divided by time. In this equation, s stands for speed, d stands for distance and t stands for time: s = d / t.
Solving for Rate (Speed)
One way to use the equation for speed is to calculate the speed of a traveling object. For example, a car travels 400 miles in seven hours and you want to know how fast, on average, the car traveled. Using the equation s = d / t, plug in the distance of 400 miles for d and time of seven hours in for t: s = 400 miles / 7 hours = 57.1 miles/hour.
Solving for Distance
To solve for distance instead of speed, imagine the car travels at 40 miles per hour for 2.5 hours. To find the distance the car traveled, you must rearrange the rate equation to solve for d. Start by multiplying both sides by t. Once you've done that, d will be by itself on the right side. The equation now looks like this: d = s x t. Now just plug in your values for speed and time to solve for distance: d = 40 miles/hour x 2.5 hours = 100 miles.
Solving for Time
Like solving for distance, solving for time involves rearranging the speed equation. But this time there are two rearranging steps instead of one. To get t alone, you must first multiply both sides by t, then divide both sides by s. Now t will be alone on the left side of the equation: t = d / s
Imagine the car travels 350 miles at an average speed of 65 miles per hour and you want to know how long the trip took. Plug the values for distance and speed into the newly rearranged equation: t = 350 miles / 65 miles/hour = 5.4 hours.
- Photo Credit John Lund/Paula Zacharias/Blend Images/Getty Images
How to Calculate Growth Rate or Percent Change
A percent growth rate -- sometimes referred to as percent change, growth rate or rate of change -- is a useful indicator...
How To Calculate an Incident Rate
Calculating Incident Rate may be required by OSHA and/or MSHA. It is also a good way of seeing your company's safety performance...
How to Calculate Interest Rates
A list of things that make many people cringe might include interest rates and math. Whether you're learning about interest rates in...
How to Use Calculus to Find the Total Distance Traveled
You can find the total distance traveled by an object in two- or multi-dimensional space by using integral calculus. Integration is a...
How to Calculate Distance Traveled from MPH
How to Calculate Distance Traveled from MPH. ... you need only the time you traveled to calculate your distance.Use this formula for...
How to Calculate Field Goal Distance
Field goals are important in American professional football and can be the difference in a game, yet calculating their distance can be...
How to Calculate Success Rate
Success rate is a term used in statistics that you can apply to many different areas. The success rate looks at a...
How to Calculate Miles Traveled
How to Calculate Distance Traveled from MPH. How far you go in a given time depends on your speed. In the United...
How to Calculate Distance Angle
The angle of elevation is the angle between an imaginary horizontal line and a person's line of sight focused on an object...
How to Calculate Average Rate
Whether you're calculating a rate of pay or the average rate of water flow, the math is the same. A rate is...
How to Find a Unit Rate
Knowing how to determine a unit rate comes in handy in everyday life and in business. The unit rate is a way...