SOLVING UNIT RATE PROBLEMS

Problem 2 :

Four gallons of gasoline cost $16.80. What is the price per gallon?

Solution :

Cost of 4 gallons of gasoline = $16.80

Cost of 1 gallon = 16.80 / 4

= $4.20

Problem 3 :

A T-shirt launcher can launch 5 shirts in 20 minutes. What is the rate in shirts per hour?

Solution :

Number of T shirts launched in 20 minutes = 5

1 hour = 60 minutes

20 minutes = 5 shirts

Multiplying both sides by 3, we get

20(3) minutes = 5(3) shirts

60 minutes = 15 shirts

So, in one hour they may launch 15 shirts.

Problem 4 :

Four gallons of gasoline cost $16.80.

(a) What is the price per gallon?

(b) What is the price of gasoline in terms of gallons per dollar?

Solution :

(a) Cost of 4 gallons of gasoline = $16.80

Cost of 1 gallon of gasoline = 16.80/4

= $4.2

Cost of 1 gallon of gasoline is $4.2

(b) If we spend $16.80, we will get 4 gallons of gasoline.

$1 = 4/16.80

$1 = 0.238 gallons

Problem 5 :

Ashley needs to ride her bike to her friend’s house 96 miles away. She is riding at an average rate of 15 miles per hour. She has 6 hours to get there. Will she make it?

Solution :

Distance to be covered = 96 miles.

Average rate = 15 miles per hour.

Time given = 6 hours

Distance = Time x speed

= 15 x 6

= 90

She can cover 90 miles in the time duration.

Problem 6 :

Ed drives from Jefferson to Holden, a distance of 250 miles. He then travels on to Paxton, which is 50 miles from Holden. If it takes him 5 hours to complete the entire trip, how fast was he traveling if he is traveling at a constant speed?

Solution :

Distance from Jefferson to Holden = 250 miles

Distance from Holden to Paxton = 50 miles

Total distance to be covered = 250 + 50

= 300 miles

Time taken = 5 hours

Time = Distance / Speed

Speed = Distance / Time

Speed = 300 / 5

Constant speed is 60 miles per hour.

Problem 7 :

Which is the best buy?

Offer A : 6 shirts for $25.50

Offer B : 4 shirts for $18.00

Offer C : 5 shirts for $21

Solution :

Offer A :

Cost of 6 shirts = $25.50

Cost of 1 shirt = 25.50/6 ==> $4.25

Offer B :

Cost of 4 shirts = $18

Cost of 1 shirt = 18/4 ==> $4.5

Offer C :

Cost of 5 shirts = $21

Cost of 1 shirt = 21/5 ==> $4.2

So, offer C is the best offer.

Problem 8 :

Lauren took 12 hours to read a 360 page book. At this rate, how long will it take her to read a 400 page book?

Solution :

Time taken to read the book consists of 360 pages

= 12 hours

To read 1 page, he will take 12/360 hours

To read 400 pages, he will take 400 (12/360) hours

= 13.3 hours.

Problem 9 : 

Pat wants to enter a typing contest.  In order to enter, one has to be able to type 50 words per minute. Pat took 15 seconds to type 10 words. Can he enter the contest?

Solution : 

Number of words should be typed in 1 minute = 50

60 minutes = 50 words

Number word he can type = 10

15 seconds = 10 words

Multiplying by 4 on both sides

60 seconds = 40 words

360 seconds = 240 words

So, he can enter the contest.

Problem 10 :

Five lemons cost $1.80.

a) What is the cost per lemon?

b) At this rate, what is the cost of 9 lemons?

Solution :

a) Cost of 5 lemons = $1.80

Cost of 1 lemon = 1.80/5

= $0.36

b) Cost of 9 lemons = 9(0.36)

= $3.24