3.1E: Exercises
- Last updated
- Jan 6, 2020
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Practice Makes Perfect
Use the Distance, Rate, and Time Formula
In the following exercises, solve.
Exercise 3.1E.1
Steve drove for 812 hours at 72 miles per hour. How much distance did he travel?
Exercise 3.1E.2
Socorro drove for 456 hours at 60 miles per hour. How much distance did she travel?
- Answer
-
290 miles
Exercise 3.1E.3
Yuki walked for 134 hours at 4 miles per hour. How far did she walk?
Exercise 3.1E.4
Francie rode her bike for 212 hours at 12 miles per hour. How far did she ride?
- Answer
-
30 miles
Exercise 3.1E.5
Connor wants to drive from Tucson to the Grand Canyon, a distance of 338 miles. If he drives at a steady rate of 52 miles per hour, how many hours will the trip take?
Exercise 3.1E.6
Megan is taking the bus from New York City to Montreal. The distance is 380 miles and the bus travels at a steady rate of 76 miles per hour. How long will the bus ride be?
- Answer
-
5 hours
Exercise 3.1E.7
Aurelia is driving from Miami to Orlando at a rate of 65 miles per hour. The distance is 235 miles. To the nearest tenth of an hour, how long will the trip take?
Exercise 3.1E.8
Kareem wants to ride his bike from St. Louis to Champaign, Illinois. The distance is 180 miles. If he rides at a steady rate of 16 miles per hour, how many hours will the trip take?
- Answer
-
11.25 hours
Exercise 3.1E.9
Javier is driving to Bangor, 240 miles away. If he needs to be in Bangor in 4 hours, at what rate does he need to drive?
Exercise 3.1E.10
Alejandra is driving to Cincinnati, 450 miles away. If she wants to be there in 6 hours, at what rate does she need to drive?
- Answer
-
75 mph
Exercise 3.1E.11
Aisha took the train from Spokane to Seattle. The distance is 280 miles and the trip took 3.5 hours. What was the speed of the train?
Exercise 3.1E.12
Philip got a ride with a friend from Denver to Las Vegas, a distance of 750 miles. If the trip took 10 hours, how fast was the friend driving?
- Answer
-
75 mph
Solve a Formula for a Specific Variable
In the following exercises, use the formula d=rt.
Exercise 3.1E.13
Solve for t
- when d=350 and r=70
- in general
Exercise 3.1E.14
Solve for t
- when d=240 and r=60
- in general
- Answer
-
- t=4
- t=dr
Exercise 3.1E.15
Solve for t
- when d=510 and r=60
- in general
Exercise 3.1E.16
Solve for t
- when d=175 and r=50
- in general
- Answer
-
- t=3.5
- t=dr
Exercise 3.1E.17
Solve for r
- when d=204 and t=3
- in general
Exercise 3.1E.18
Solve for r
- when d=420 and t=6
- in general
- Answer
-
- r=70
- r=dt
Exercise 3.1E.19
Solve for r
- when d=160 and t=2.5
- in general
Exercise 3.1E.20
Solve for r
- when d=180 and t=4.5
- in general
- Answer
-
- r=40
- r=dt
In the following exercises, use the formula A=12bh
Exercise 3.1E.21
Solve for b
- when A=126 and h=18
- in general
Exercise 3.1E.22
Solve for h
- when A=176 and b=22
- in general
- Answer
-
- h=16
- h=2Ab
Exercise 3.1E.23
Solve for h
- when A=375 and b=25
- in general
Exercise 3.1E.24
Solve for b
- when A=65 and h=13
- in general
- Answer
-
- b=10
- b=2Ah
In the following exercises, use the formula I=Prt.
Exercise 3.1E.25
Solve for the principal, P for
- I=$5,480, r=4%, t=7 years
- in general
Exercise 3.1E.26
Solve for the principal, P for
- I=$3,950, r=6%, t=5 years
- in general
- Answer
-
- P=$13,166.67
- P=Irt
Exercise 3.1E.27
Solve for the time, t for
- I=$2,376, P=$9,000, r=4.4%
- in general
Exercise 3.1E.28
Solve for the time, t for
- I=$624, P=$6,000, r=5.2%
- in general
- Answer
-
- t=2 years
- t=IPr
In the following exercises, solve.
Exercise 3.1E.29
Solve the formula 2x+3y=12 for y
- when x=3
- in general
Exercise 3.1E.30
Solve the formula 5x+2y=10 for y
- when x=4
- in general
- Answer
-
- y=−5
- y=10−5x2
Exercise 3.1E.31
Solve the formula 3x−y=7 for y
- when x=−2
- in general
Exercise 3.1E.32
Solve the formula 4x+y=5 for y
- when x=−3
- in general
- Answer
-
- y=17
- y=5−4x
Exercise 3.1E.33
Solve a+b=90 for b.
Exercise 3.1E.34
Solve a+b=90 for a
- Answer
-
a=90−b
Exercise 3.1E.35
Solve 180=a+b+c for a
Exercise 3.1E.36
Solve 180=a+b+c for c
- Answer
-
c=180−a−b
Exercise 3.1E.37
Solve the formula 8x+y=15 for y
Exercise 3.1E.38
Solve the formula 9x+y=13 for y
- Answer
-
y=13−9x
Exercise 3.1E.39
Solve the formula −4x+y=−6 for y
Exercise 3.1E.40
Solve the formula −5x+y=−1 for y
- Answer
-
y=−1+5x
Exercise 3.1E.41
Solve the formula 4x+3y=7 for y
Exercise 3.1E.42
Solve the formula 3x+2y=11 for y
- Answer
-
y=11−3x2
Exercise 3.1E.43
Solve the formula x−y=−4 for y
Exercise 3.1E.44
Solve the formula x−y=−3 for y
- Answer
-
y=3+x
Exercise 3.1E.45
Solve the formula P=2L+2W for L
Exercise 3.1E.46
Solve the formula P=2L+2W for W
- Answer
-
W=P−2L2
Exercise 3.1E.47
Solve the formula C=πd for d
Exercise 3.1E.48
Solve the formula C=πd for π
- Answer
-
π=Cd
Exercise 3.1E.49
Solve the formula V=LWH for L
Exercise 3.1E.50
Solve the formula V=LWH for H
- Answer
-
H=VLW
Everyday Math
Exercise 3.1E.51
Converting temperature While on a tour in Greece, Tatyana saw that the temperature was 40o Celsius. Solve for F in the formula C=59(F−32) to find the Fahrenheit temperature.
Exercise 3.1E.52
Converting temperature Yon was visiting the United States and he saw that the temperature in Seattle one day was 50oFahrenheit. Solve for C in the formula F=95C+32 to find the Celsius temperature.
- Answer
-
10∘C
Writing Exercises
Exercise 3.1E.53
Solve the equation 2x+3y=6 for y
- when x=−3
- in general
- Which solution is easier for you, 1 or 2? Why?
Exercise 3.1E.54
Solve the equation 5x−2y=10 for x
- when y=10
- in general
- Which solution is easier for you, 1 or 2? Why?
- Answer
-
Answers will vary.
Self Check
ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
ⓑ What does this checklist tell you about your mastery of this section? What steps will you take to improve?