Go through the **Spectrum Math Grade 6 Answer Key Chapter 3 Lesson 3.4 Understanding Unit Rates** and get the proper assistance needed during your homework.

## Spectrum Math Grade 6 Chapter 3 Lesson 3.4 Understanding Unit Rates Answers Key

A rate is a special ratio that compares quantities of two different types of items—for example, 340 miles per 10 gallons (340 mi./10 gal.). In a unit rate, the second quantity is always I, such as in 34 miles per gallon (34 mi./l gal.). This allows you to see how many of the first item corresponds to just one of the second item.

Suppose you want to divide students equally between buses for a field trip. To see how many students should go on each bus, find the unit rate.

If there are 160 students and 4 buses, how many students should go on each bus?

\(\frac{160}{4}\) = \(\frac{s}{1}\) To find the number of students for one bus, divide by the number of buses total.

\(\frac{160}{4}\) = \(\frac{40}{1}\) The unit rate is \(\frac{40}{1}\), or 40 students per bus.

**Solve each problem by finding the unit rate.**

Question 1.

John can create 20 paintings in 4 weeks. How many paintings can he create each week?

Answer:

Number of paintings can he create each week = 5.

Explanation:

Number of paintings John can create = 20.

Number of weeks = 4.

Let the number of paintings can he create each week be S.

=> \(\frac{20}{4}\) = \(\frac{S}{1}\)

=> 20 × 1 = S × 4

=> 20 = 4S

=> 20 ÷ 4 = S

=> 5 = S.

Question 2.

Sasha can walk 6 miles in 3 hours. If she has to walk 1 mile, how long will it take her?

Answer:

Number of hours she takes to walk 1 mile = 2.

Explanation:

Number of miles Sasha can walk = 6.

Number of hours she can walk = 3.

Let the hours she takes to walk 1 mile be X.

=> \(\frac{6}{3}\) = \(\frac{X}{1}\)

=> 6 × 1 = X × 3

=> 6 = 3X

=> 6 ÷ 3 = X

=> 2 = X.

Question 3.

Todd keeps his 4-room house very clean. It takes him 1 hour and 36 minutes to clean his whole house. How long does it take him to clean one room?

Answer:

Time it takes him to clean one room = 24.

Explanation:

Number of rooms Todd keeps cery clean = 4.

Number of hours to clean his whole house = 1hour 36 minutes = 96 minutes.

Let the time it takes him to clean one room be S.

=> \(\frac{90}{4}\) = \(\frac{S}{1}\)

=> 96 × 1 = S × 4

=> 96 = 4S

=> 96 ÷ 4 = S

=> 24 minutes = S.

Question 4.

Victoria can make 8 necklaces in 4 days. How long does it take her to make one necklace?

Answer:

Number of days it takes her to make one necklace = 2.

Explanation:

Number of necklaces Victoria can make = 8.

Number of days = 4.

Let the number of days it takes her to make one necklace be X.

=> \(\frac{8}{4}\) = \(\frac{S}{1}\)

=> 8 × 1 = S × 4

=> 8 = 4S

=> 8 ÷ 4 = S

=> 2 = S.

Question 5.

Byron has his own bakery. He bakes 84 cakes each week. How many cakes can he make in one day?

Answer:

Number of cakes he makes in one day = 12.

Explanation:

Number of cakes he bakes = 84.

Number of days he bakes them = 7.

Let the number of cakes he makes in one day be X.

=> \(\frac{84}{7}\) = \(\frac{X}{1}\)

=> 84 × 1 = X × 7

=> 84 = 7X

=> 84 ÷ 7 = X

=> 12 = X.

Question 6.

Charlie buys 3 computer tables for $390. How much did he pay for each table?

Answer:

Cost of each computer table he pays = $130.

Explanation:

Number of computer tables Charlie buys = 3.

Cost of computer tables he buys = $390.

Let the cost of each computer table he pays be S.

=> \(\frac{390}{3}\) = \(\frac{S}{1}\)

=> 390 × 1 = S × 3

=> 390 = 3S

=> 390 ÷ 3 = S

=> $130 = S.