**Unit Rate Definition :**

Unit rate compares the given amount to one unit of another measure

(or)

The ratio between the given value and 1

(or)

Comparing the given amount or value to 1

**Examples :**

1. If 8 dolls are made in 4 days,

then number of dolls made in 1 day = 2

2. If David earns $180 in 9 hours,

then number of dollars earned by him in 1 hour = $ 20

3. If there are 16 cups in 4 quarts,

then the number of cups in 1 quart = 4.

From the above picture, we can get the following unit rates related to liquid measurements.

1 gallon = 16 cups

1 gallon = 8 pints

1 gallon = 4 quarts

1 quart = 2 pints

1 quart = 4 cups

1 pint = 2 cups

**Problem 1 :**

In a business, if A can earn $ 7500 in 2.5 years, find the unit rate of his earning per month.

**Solution : **

**Given :** Earning in 2.5 years = $ 7500

1 year = 12 months

2.5 years = 2.5 x 12 = 30 months

Then, earning in 30 months = $ 7500

Therefore, earning in 1 month = 7500 / 30 = $250

Hence, the unit rate of his earning per month is $250.

**Problem 2 :**

If David can prepare 2 gallons of juice in 4 days, how many cups of juice can he prepare per day ?

**Solution : **

No of gallons of juice prepared in 4 days = 2 gallons

1 gallon = 16 cups

So, no. of cups of juice prepared in 4 days = 2 ⋅ 16 = 32 cups

Therefore, David can prepare 32 cups of juice in 4 days.

Then, no. of cups of juice prepared in 1 day = 32 / 4 = 8

Hence, David can prepare 8 cups of juice in 1 day.

**Problem 3 :**

If John can cover 360 miles in 3 hours, find the number of miles covered by John in 1 minute.

**Solution : **

No of miles covered in 3 hours = 360

Then, no. of miles covered in 1 hour = 360 / 3 = 180

1 hour = 60 minutes

So, no. of miles covered in 60 minutes = 180

Then, no. of miles covered 1 minute = 180 / 60 = 3

Hence, John can cover 3 miles in 1 minute.

**Problem 4 : **

75 basketballs cost $1,143.75. Find the unit rate in price per basketball.

**Solution : **

**Given :**75 basketballs cost $1,143.75

Then, price pf one basket ball = 1143.75 / 75 = 15.25

Hence, the unit rate in price per basket ball is $ 15.25.

**Problem 5 :**

In 36.5 weeks, Miguel raised $2,372.50 for cancer research. How was his unit rate in price per week?

**Solution :**

**Given :** Miguel raised $2, 372.50 in 36.5 weeks

Then, amount raised in one week = 2372.5 / 36.5 = 65

Hence, the unit rate in price per week was $65.

**Problem 6 : **

Shanel walks 2/5 of a mile every 1/7 hour. Express her speed as a unit rate in miles per hour.

**Solution : **

**Given :**Shanel walks 2/5 of a mile every 1/7 hour

We know the formula for speed.

That is, Speed = Distance / time

Speed = (2/5) / (1/7)

Speed = (2/5) ⋅ (7/1)

Speed = 14 / 5

Speed = 2.8 miles per hour

Hence, the speed of Shanel is 2.8 miles per hour.

**Problem 7 : **

Declan use 2/35 of a gallon of gas for every 4/5 of a mile that he drives. At this rate, how many miles can he drive on one gallon of gas?

**Solution : **

**Given : **In 2/35 of a gallon of gas, 4/5 of a mile is traveled

2/35 of a gallon of gas -----> 4/5 of a mile

1 gallon of gas -----> (4/5) ⋅ (35/2) miles

1 gallon of gas -----> 14 miles

Hence, Declan can drive 14 miles in 1 gallon of gas.

**Problem 8 : **

A person can cover a distance of 84 miles in 4 gallons of fuel. If he has 2.5 gallons, how many miles can he cover ?

**Solution : **

**Given :** 84 miles can be traveled in 4 gallons.

Then, no. of miles traveled in 1 gallon = 84/4 = 21

Therefore, no. of miles traveled in 2.5 gallons is

= 21 ⋅ 2.5

= 52.5

Hence, 52.5 miles traveled in 2.5 gallons of fuel.

**Problem 9 : **

If a person drinks 8 cups of apple juice per month, how many gallons will he drink in one year?

**Solution : **

**Given :**8 cups in one month

1 year = 12 months

So, no. of cups in 1 year = 8 ⋅ 12 = 96 cups

1 gallon = 16 cups

Therefore, no. of gallons in 1 year = 96/16 = 6

Hence, he will drink 6 gallons of apple juice in 1 year.

**Problem 10 :**

My David earns $416 in 8 hours. How much does earn in 2.8 hours ?

**Solution : **

**Given :** Earning in 8 hours = $ 416

Earning in 1 hour = $ 52

Earning in 2.8 hours = 52 ⋅ 2.8 = 145.6

Hence, Mr. David will earn $145.6 in 2.8 hours.

After having gone through the stuff given above, we hope that the students would have understood the definition of unit rate.

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

Widget is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**

**Sum of all three four digit numbers formed using 0, 1, 2, 3**

**Sum of all three four digit numbers formed using 1, 2, 5, 6**

HTML Comment Box is loading comments...