# USING UNIT RATES TO SOLVE PROBLEMS WORKSHEET

Problem 1 :

David covers 600 miles in 8 hours and John covers 380 miles in 5 hours. Who is driving faster ?

Problem 2 :

Michael is at the grocery store comparing two brands of juice. Brand A costs \$3.84 for a 16-ounce bottle. Brand B costs \$4.50 for a 25-ounce bottle. Which brand is the better buy ?

Problem 3 :

Jacob can do 200 units work in 8 days whereas Mathew can do 130 units of work in 5 days. Who is better ?

Problem 4 :

Lily has two job offers. One is paying \$160 for 8 hours and other one is paying \$95 for 5 hours. Can you help Lily to choose the better job ?

Problem 1 :

David covers 600 miles in 8 hours and John covers 380 miles in 5 hours. Who is driving faster ?

Solution :

Distance covered by David in 1 hour is

=  600 / 8

=  75 miles per hour

Distance covered by John in 1 hour is

=  380 / 5

=  76 miles per hour

When we compare the above unit rates (Distance covered in 1 hour), John is driving faster than David.

Problem 2 :

Michael is at the grocery store comparing two brands of juice. Brand A costs \$3.84 for a 16-ounce bottle. Brand B costs \$4.50 for a 25-ounce bottle. Which brand is the better buy ?

Solution :

To compare the costs, Michael must compare prices for equal amounts of juice.

That is, he has to compare prices of one ounce of each juice.

We can get the price of 1 ounce of each juice as given below.

From the above tables,

Brand A costs  =  \$0.24 per ounce

Brand B costs  =  \$0.18 per ounce

When we compare the unit prices of the two brands given above, it is better to buy brand B.

Problem 3 :

Jacob can do 200 units work in 8 days whereas Mathew can do 130 units of work in 5 days. Who is better ?

Solution :

To compare Jacob and Mathew, We have to convert the given quantities into unit rates.

That is, we have calculate the amount of work done by them per day.

Number of units of work done by Jacob is

=  200 / 8  =  25 units per day

Number of units of work done by Mathew is

=  130 / 5  =  26 units per day

When we compare the above unit rates (work done per day), Mathew is better.

Problem 4 :

Lily has two job offers. One is paying \$160 for 8 hours and other one is paying \$95 for 5 hours. Can you help Lily to choose the better job ?

Solution :

In both the jobs, salary is given for different hours. To compare the two jobs, we have to convert the salaries into unit rates.

That is, we have to find the salary for 1 hour.

In job 1 ,

Salary for 1 hour  =  160/8  =  \$20 per hour

In job 2 ,

Salary for 1 hour  =  95/5  =  \$19 per hour

Conclusion :

When we compare the unit rates of both the jobs, Lily gets \$1 more in the first job.

Hence, the first job is preferable.

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WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

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

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

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

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

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

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