Rate is a very important type of ratio, used in many everyday problems, such as grocery shopping, traveling, medicine--in fact, almost every activity involves some type of rate. Miles per hour or feet per second are both rates of speed. Number of heartbeats per minute is called "heart rate." If you ask a babysitter, "What is your rate?", you are asking how many dollars per hour you will be charged. The little word "per" is always a clue that you are dealing with a rate. Unit price is a particular rate that compares a price to some unit of measure. For example, suppose eggs are on sale for $.72 per dozen. The unit price is $.72 divided by 12, or 6 cents per egg.
The word "per" can be replaced by the "/" in problems, so 6 cents per egg can also be written 6 cents/egg.
Smart shoppers know how to estimate unit prices when deciding whether it's better to buy a larger size of an item. Many everyday problems involve rates of speed, using distance and time. We can solve these problems using proportions and cross products. However, it's easier to use a handy formula: rate equals distance divided by time: r = d/t. Actually, this formula comes directly from the proportion calculation -- it's just that one multiplication step has already been done for you, so it's a shortcut to learn the formula and use it. You can write this formula in two other ways, to solve for distance (d = rt) or time (t = d/r).
Examples
Let's say you rode your bike 2 hours and traveled 24 miles. What is your rate of speed? Use the formula r = d/t. Your rate is 24 miles divided by 2 hours, so:
r = 24 miles ÷ 2 hours = 12 miles per hour.
Now let's say you rode your bike at a rate of 10 miles per hour for 4 hours. How many miles did you travel? This time, use the distance formula d = rt:
d = 10 miles per hour × 4 hours = 40 miles.
Next, you ride 18 miles and travel at a rate of 12 miles per hour. How long did this take you? Use the time formula t = d/r:
t = 18 miles ÷ 12 miles per hour = 1.5 hours, or 1 ½ hours.
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FAQs
The two terms a and d are known as extreme terms. The proportion formula can be expressed as, a/b = c/d or a : b : : c : d.
How do you find the ratio of distance to time? ›
That is speed = distance ÷ time. Or to put it another way distance divided by speed will give you the time. Provided you know two of the inputs you can work out the third. For example if a car travels for 2 hours and covers 120 miles we can work out speed as 120 ÷ 2 = 60 miles per hour.
What is ratio answers? ›
A ratio is a way of comparing two or more similar quantities. A ratio of 2 cm to 5 cm is written as 2 : 5. A ratio is normally written using whole numbers only, with no units, in its simplest form. The numbers in a ratio must be written using the same units. If they are not, they should be converted to the same units.
How do I calculate a rate? ›
Calculate the rate
Subtract the starting time from the ending time to find the total length of the interval. Divide the total change by the interval length to find the rate of change over the course of the interval.
How do you solve for rates? ›
How do you calculate rate in math? Rate is defined as the change in one unit divided by the change in a second unit. For example, to find the rate of change in miles per hour, divide the number of miles traveled by the amount of time traveled.
What is a rate in math? ›
In mathematics, a rate is a comparison between two quantities with different units, expressed as a ratio representing the amount of one quantity per unit of another. Rate can be defined as a ratio that expresses the comparison of two different quantities which have different units.
What is ratio and time? ›
If two objects have their speeds in the ratio a:b, distance covered by the two objects in same time will be in the ratio a:b and time taken by the two objects to cover same distance will be in the ratio b:a. The ratio concept can be applied only when one of the given distance, time or speed is constant.
What is speed times time? ›
distance = speed × time. time = distance ÷ speed.
What is an example of a rate ratio and proportion? ›
For example, you need to mix different colours of paint in a specific ratio to get a desired colour. When we say we are driving 100 kilometers per hour, that is an example of a rate. If two rates or ratios are equivalent to one another it is called a proportion.
How do you solve distance rate and time problems? ›
When solving these problems, use the relationship rate (speed or velocity) times time equals distance. For example, suppose a person were to travel 30 km/h for 4 h. To find the total distance, multiply rate times time or (30km/h)(4h) = 120 km.
Speed (or rate, r) is a scalar quantity that measures the distance traveled (d) over the change in time (Δt), represented by the equation r = d/Δt.
How do you calculate time? ›
FAQs on Time Formula
The formula for time is given as [Time = Distance ÷ Speed]. To calculate the distance, the time formula can be molded as [Distance = Speed × Time].
How do you write an answer for a proportion? ›
To write a proportion, set two equivalent fractions equal to each other, using the information in the problem. For example, if you know the ratio of girls to boys in a class is 2 : 3, and you know there are 24 boys in the class, you can write a proportion in order to find the number of girls in the class.
What is an example of a ratio and proportion? ›
A proportion is a type of ratio that relates a part to a whole. For example, in the class with with 20 men and 80 women, the total class size is 100, and the proportion of men is 20/100 or 20%. The proportion of women is 80/100 or 80%.
How do you write a ratio answer? ›
Ratios can be written 3 different ways:
- Using the : symbol — 2:5.
- As a common fraction — 25. The first number in the ratio is the numerator; the second number is the denominator. Ratios written as a common fraction are read as a ratio, not as a fraction. Say “2 to 5,” not “two-fifths.”
- Using the word “to” — 2 to 5.
