2.2 Module 4 Lesson 11
Lesson 11: Constant Rate Notes
Pauline mows a lawn at a constant rate. Suppose she mows a 𝟑𝟓 square foot lawn in 𝟐. 𝟓 minutes.
What area, in square feet, can she mow in 𝟏𝟎 minutes? 𝒕 minutes?
35

Pauline’s average rate in 2.5 minutes is 2.5 square feet per minute.

Let 𝐴 represent area mowed. Pauline’s average rate in 10 minutes is
𝐴
10
square feet per
mintute.
Therefore,
𝟑𝟓
𝑨
=
𝟐. 𝟓 𝟏𝟎
𝟑𝟓𝟎 = 𝟐. 𝟓𝑨
𝟑𝟓𝟎 𝟐. 𝟓
=
𝑨
𝟐. 𝟓 𝟐. 𝟓
𝟏𝟒𝟎 = 𝑨
Pauline mows 𝟏𝟒𝟎 square feet of lawn in 𝟏𝟎 minutes.
𝒕 (time in
minutes)
Linear equation:
𝟑𝟓
𝒚=
𝒕
𝟐. 𝟓
𝟑𝟓
𝒚=
(𝟎)
𝟐. 𝟓
𝟑𝟓
(𝟏)
𝒚=
𝟐. 𝟓
𝟑𝟓
(𝟐)
𝒚=
𝟐. 𝟓
𝟑𝟓
(𝟑)
𝒚=
𝟐. 𝟓
𝟑𝟓
(𝟒)
𝒚=
𝟐. 𝟓
1.
𝟎
𝟏
𝟐
𝟑
𝟒
𝒚
(area in
square feet)
2.
𝟎
𝟑𝟓
= 𝟏𝟒
𝟐. 𝟓
𝟕𝟎
= 𝟐𝟖
𝟐. 𝟓
𝟏𝟎𝟓
= 𝟒𝟐
𝟐. 𝟓
𝟏𝟒𝟎
= 𝟓𝟔
𝟐. 𝟓
Water flows at a constant rate out of a faucet. Suppose the volume of water that comes out in three
minutes is 𝟏𝟎. 𝟓 gallons. How many gallons of water comes out of the faucet in 𝒕 minutes?
Let 𝑪 represent the constant rate of water flow.
𝟏𝟎.𝟓
𝟑
= 𝑪 and
𝑽
𝒕
= 𝑪, then
𝟏𝟎.𝟓
𝟑
𝑽
= 𝒕.
𝟏𝟎. 𝟓 𝑽
=
𝟑
𝒕
𝟑𝑽 = 𝟏𝟎. 𝟓𝒕
𝟑
𝟏𝟎. 𝟓
𝑽=
𝒕
𝟑
𝟑
𝟏𝟎. 𝟓
𝑽=
𝒕
𝟑

2.2 Module 4 Lesson 11
Using the linear equation 𝑉 =
𝒕 (time in minutes)
𝟎
𝟏
𝟐
𝟑
𝟒
complete the table:
Linear equation:
𝟏𝟎. 𝟓
𝑽=
𝒕
𝟑
𝟏𝟎. 𝟓
𝑽=
(𝟎)
𝟑
𝟏𝟎. 𝟓
(𝟏)
𝑽=
𝟑
𝟏𝟎. 𝟓
(𝟐)
𝑽=
𝟑
𝟏𝟎. 𝟓
(𝟑)
𝑽=
𝟑
𝟏𝟎. 𝟓
(𝟒)
𝑽=
𝟑
17
𝑽 (in gallons)
16
15
𝟎
14
𝟏𝟎. 𝟓
= 𝟑. 𝟓
𝟑
𝟐𝟏
=𝟕
𝟑
𝟑𝟏. 𝟓
= 𝟏𝟎. 𝟓
𝟑
𝟒𝟐
= 𝟏𝟒
𝟑
13
Volume of water in gallons, 𝑉

10.5
𝑡,
3
12
11
10
9
8
7
6
5
4
3
2
1
0
1
2
3
4
5
6
7
Time in minutes, 𝑡
𝟏
Jesse types at a constant rate. He can type a full page of text in 𝟑 minutes. We want to know how
𝟐
many pages, 𝒑, Jesse can type after 𝒕 minutes.
a. Write the linear equation in two variables that represents the number of pages Jesse types in any given
time interval.
3.
Let C represent the constant rate that Jesus types. Then,
𝟏
𝟑.𝟓
= 𝑪 and
𝒑
𝒕
𝟏
𝒑
= 𝑪, therefore 𝟑.𝟓 = 𝒕 .
𝟏
𝒑
=
𝟑. 𝟓 𝒕
𝟑. 𝟓𝒑 = 𝒕
𝟑. 𝟓
𝟏
𝒑=
𝒕
𝟑. 𝟓
𝟑. 𝟓
𝟏
𝒑=
𝒕
𝟑. 𝟓
8
9
10
2.2 Module 4 Lesson 11
Complete the table below. Use a calculator and round answers to the tenths place.
Linear equation:
𝟏
𝒑=
𝒕
𝟑. 𝟓
𝟏
𝒑=
(𝟎)
𝟑. 𝟓
𝟏
(𝟓)
𝒑=
𝟑. 𝟓
𝟏
(𝟏𝟎)
𝒑=
𝟑. 𝟓
𝟏
(𝟏𝟓)
𝒑=
𝟑. 𝟓
𝟏
(𝟐𝟎)
𝒑=
𝟑. 𝟓
𝒕 (time in
minutes)
𝟎
𝟓
𝟏𝟎
𝟏𝟓
𝟐𝟎
𝒑 (pages typed)
10
9
8
𝟎
Pages typed, 𝑝
a.
𝟓
≅ 𝟏. 𝟒
𝟑. 𝟓
𝟏𝟎
≅ 𝟐. 𝟗
𝟑. 𝟓
𝟏𝟓
≅ 𝟒. 𝟑
𝟑. 𝟓
𝟐𝟎
≅ 𝟓. 𝟕
𝟑. 𝟓
7
6
5
4
3
2
1
0
1
2
3
4
5
6
7
8
9
10
11 12 13 14 15
16 17
Time in minutes, 𝑡
b.
About how long would it take Jesse to type a 𝟓-page paper? Explain.
Approximately 1.4 minutes.
4.
Emily paints at a constant rate. She can paint 𝟑𝟐 square feet in five minutes. What area, 𝑨, can she
paint in 𝒕 minutes?
Write the linear equation in two variables that represents the number of square feet Emily
can paint in any given time interval.
Let 𝑪 be the constant rate that Emily paints. Then,
𝟑𝟐
𝟓
= 𝑪 and
𝑨
𝒕
= 𝑪, therefore
𝟑𝟐
𝟓
𝑨
= 𝒕.
𝟑𝟐 𝑨
=
𝟓
𝒕
𝟓𝑨 = 𝟑𝟐𝒕
𝟓
𝟑𝟐
𝑨=
𝒕
𝟓
𝟓
𝟑𝟐
𝑨=
𝒕
𝟓
Complete the table below. Use a calculator and round answers to the tenths place.
t (time in
minutes)
𝟎
𝟏
𝟐
𝟑
𝟒
Linear equation:
𝟑𝟐
𝑨=
𝒕
𝟓
𝟑𝟐
𝑨=
(𝟎)
𝟓
𝟑𝟐
(𝟏)
𝑨=
𝟓
𝟑𝟐
(𝟐)
𝑨=
𝟓
𝟑𝟐
(𝟑)
𝑨=
𝟓
𝟑𝟐
(𝟒)
𝑨=
𝟓
𝑨 (area
painted in
square feet)
𝟎
𝟑𝟐
= 𝟔. 𝟒
𝟓
𝟔𝟒
= 𝟏𝟐. 𝟖
𝟓
𝟗𝟔
= 𝟏𝟗. 𝟐
𝟓
𝟏𝟐𝟖
= 𝟐𝟓. 𝟔
𝟓
26
24
22
Area painted in square feet, 𝐴
b.
20
18
16
14
12
10
8
6
4
2
0
1
2
3
4
5
6
7
Time in minutes, 𝑡
8
9
10
18 19
20 21
2.2 Module 4 Lesson 11
c.
𝟏
About how many square feet can Emily paint in 𝟐 𝟐 minutes? Explain.
𝟏
Emily can paint between 𝟏𝟐. 𝟖 and 𝟏𝟗. 𝟐 square feet in 𝟐 𝟐 minutes. After 𝟐 minutes she paints 𝟏𝟐. 𝟖
square feet and at 𝟑 minutes she will have painted 𝟏𝟗. 𝟐 square feet.
Joseph walks at a constant speed. He walked to the store, one-half mile away, in 𝟔 minutes. How many
miles, 𝒎, can he walk in 𝒕 minutes?
d.
Write the linear equation in two variables that represents the number of miles
Joseph can walk in any given time interval, 𝒕.
Let 𝑪 be the constant rate that Joseph walks. Then,
𝟎.𝟓
𝟔
= 𝑪 and
𝒎
𝒕
= 𝑪, therefore
𝟎.𝟓
𝟔
𝒎
= 𝒕.
𝟎. 𝟓 𝒎
=
𝟔
𝒕
𝟔𝒎 = 𝟎. 𝟓𝒕
𝟔
𝟎. 𝟓
𝒎=
𝒕
𝟔
𝟔
𝟎. 𝟓
𝒎=
𝒕
𝟔
e.
Complete the table below. Use a calculator and round answers to the tenths place.
Linear equation:
𝒕 (time in
minutes)
𝟎
𝟑𝟎
𝟔𝟎
𝟗𝟎
𝟏𝟐𝟎
𝟎. 𝟓
𝒎=
𝒕
𝟔
𝟎. 𝟓
𝒎=
(𝟎)
𝟔
𝟎. 𝟓
𝒎=
(𝟑𝟎)
𝟔
𝟎. 𝟓
𝒎=
(𝟔𝟎)
𝟔
𝟎. 𝟓
𝒎=
(𝟗𝟎)
𝟔
𝟎. 𝟓
𝒎=
(𝟏𝟐𝟎)
𝟔
𝒎 (distance
in miles)
𝟎
𝟏𝟓
= 𝟐. 𝟓
𝟔
𝟑𝟎
=𝟓
𝟔
𝟒𝟓
= 𝟕. 𝟓
𝟔
𝟔𝟎
= 𝟏𝟎
𝟔
2.2 Module 4 Lesson 11
2.2 homework
Problem Set
Lesson Summary
When constant rate is stated for a given problem, you can express the situation as a two variable equation. The
equation can be used to complete a table of values that can then be graphed on a coordinate plane.
1.
2.
3.
A train travels at a constant rate of 45 miles per hour.
a. What is the distance, 𝑑, in miles, that the train travels in 𝑡 hours?
b. How many miles will it have traveled in 2.5 hours?
1
Water is leaking from a faucet at a constant rate of 3 gallons per minute.
a. What is the amount of water, 𝑤, that is leaked from the faucet after 𝑡 minutes?
b.
How much water is leaked after an hour?
A car can be assembled on an assembly line in 6 hours. Assume that the cars are assembled at a constant
rate.
a. How many cars, 𝑦, can be assembled in 𝑡 hours?
b. How many cars can be assembled in a week?
1
A copy machine makes copies at a constant rate. The machine can make 80 copies in 2 minutes.
2
a. Write an equation to represent the number of copies, 𝑛, that can be made over any time interval, 𝑡.
b. Complete the table below.
4.
𝒕 (time in
minutes)
Linear equation:
𝒏 (number of
copies)
𝟎
𝟎. 𝟐𝟓
𝟎. 𝟓
𝟎. 𝟕𝟓
𝟏
c.
Graph the data on a coordinate plane.
The copy machine runs for 20 seconds, then jams.
About how many copies were made before the jam occurred?
Explain.
d.
Connor runs at a constant rate. It takes him 𝟑𝟒 minutes to run four miles.
Write the linear equation in two variables that represents the number of miles Connor can run in any
given time interval, 𝒕.
b. Complete the table below. Use a calculator and round answers to the tenths place.
5.
a.
2.2 Module 4 Lesson 11
𝒕 (time in minutes)
Linear equation:
𝒎 (distance in miles)
𝟎
𝟏𝟓
𝟑𝟎
𝟒𝟓
𝟔𝟎
c.
Graph the data on a coordinate plane.
d.
Connor ran for 𝟒𝟎 minutes before tripping and spraining his ankle. About how many miles did he run
before he had to stop? Explain.