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 ? 

Answers

1. Answer :

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. 

2. Answer :

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.

3. Answer :

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. 

4. Answer :

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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