A rate specifies the ratio that compares the two different quantities of different units. Example: Kilometer per Hour (kmph), Miles per Hour (mph), etc. The word per indicates that we are dealing with the rate concept. The symbolic representation of the term "per" is "/". The current topic Unit Rate also comes under the rate topic as discussed above.
Unit Rate Formula
The definition of it involves comparing a certain number of units of the first quantity to one unit of the second quantity, creating a ratio between two different measurements where the second term equals 1. Unit Rate formula has denominator 1. Suppose an example for the unit rate is there are 60 minutes in one hour. So unit rate can express 60 minutes per one (1) hour. The unit Rate formula for the two quantities/measurements A, B is given by,
Unit Rate = Ratio between two different measurements of different units
= A:B
= A/B
Let's look into a few problems on Unit Rate to get a better understanding.
Sample Questions
Question 1: If a shopkeeper gave 10 pencils to a student at a cost of 45 rupees then what is the unit cost?
Solution:
Given,
Cost of pencils student bought (A) = 45
Count of pencils (B) = 10
Unit Cost of pencil = Cost of all pencils/Count of pencils
= 45/10
= 4.5/1
So per unit cost of pencil is 4.5 rupee.
Question 2: A bike rider travel 200 km in 4hours. Apply unit rate formula to find how much distance he travels in one hour.
Solution:
Given,
Distance travelled by rider (A) = 200Km
Time taken to travel (B) = 4 hours
Unit rate Formula = Distance travelled by rider/time taken to travel
= 200/4
= 50/1
So per unit hour the rider travel 50 km. i.e., 50kmph
Question 3: In a Bookstall, Seller offers a dozen plain notebooks at a cost of 360 rupees. Find the cost of each unit?
Solution:
Given,
Cost of total books = 360 rupees
Number of books = 12
Unit rate Formula = Cost of total books/Number of books
= 360/12
= 30/1
Hence unit cost of a book is 30 rs.
Question 4: A paperboy delivers 183 newspapers in 3 hours in the early morning daily. How many papers will the paperboy distribute in an hour?
Solution:
Number of news papers distributed by a paperboy = 183
Time taken to distribute papers = 3 hours
Unit Rate formula to determine how may news paper a paper distribute in an hour is
= Number of news papers distributed/Time taken
= 183/3
= 61/1
So per unit hour a paperboy can distribute 61 newspapers.
Question 5: A car driver traveled 65km per hour on a highway. How much distance will the driver travel in a day?
Solution:
Given,
Distance travelled by a driver in an hour = 65km
A day has 24 hours, so Distance travelled by a driver in 1 day = 65 Ã 24
= 1560km
Unit rate representation of distance travelled per day = 1560/1
Question 6: Suppose there are 50 flats in an apartment containing 5 floors. How many flats will be present on a floor? (Hint- Use unit rate formula)
Solution:
Given,
Number of flats = 50
Number of floors = 5
Number of flat in each floor = Number of flats/Number of floors
= 50/5
= 10/1
Number of flat per unit floor = 10
Practice Problems
1. A machine produces 240 widgets in 8 hours. How many widgets does it produce per hour?
2. A car travels 480 miles on 16 gallons of gas. What is the car's fuel efficiency in miles per gallon?
3. A baker uses 5 cups of flour to make 2 loaves of bread. How many cups of flour are needed per loaf?
4. A water tank fills up with 300 liters of water in 10 minutes. How many liters of water fill the tank per minute?
5. A worker assembles 150 toys in 5 hours. How many toys are assembled per hour?
6. A gardener plants 90 flowers in 3 hours. What is the planting rate per hour?
7. A cyclist covers 180 kilometers in 6 hours. How many kilometers does the cyclist cover per hour?
8. A store sells 12 apples for 36 rupees. What is the cost of one apple?
9. A painter covers 150 square feet in 2 hours. What is the rate of painting per hour?
10. A delivery truck travels 600 kilometers on 15 liters of fuel. What is the truckâs fuel efficiency per liter?
Conclusion
Unit rates play an important role in our day-to-day lives and have a way of quickly comparing two quantities with different units. Whether it is the cost per item, the speed of a vehicle, or how much a machine can process, knowing how to compute and then use unit rates can sometimes simplify difficult decisions. Only using the formula for unit rate, in scenarios that follow with various problems, a good understanding can be achieved. Also remember, mastery of unit rates strengthens your problem-solving muscle and provides hands-on knowledge to make good decisions in your day-to-day activities.
