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3.1E: Exercises

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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

  1. when d=350 and r=70
  2. in general
Exercise 3.1E.14

Solve for t

  1. when d=240 and r=60
  2. in general
Answer
  1. t=4
  2. t=dr
Exercise 3.1E.15

Solve for t

  1. when d=510 and r=60
  2. in general
Exercise 3.1E.16

Solve for t

  1. when d=175 and r=50
  2. in general
Answer
  1. t=3.5
  2. t=dr
Exercise 3.1E.17

Solve for r

  1. when d=204 and t=3
  2. in general
Exercise 3.1E.18

Solve for r

  1. when d=420 and t=6
  2. in general
Answer
  1. r=70
  2. r=dt
Exercise 3.1E.19

Solve for r

  1. when d=160 and t=2.5
  2. in general
Exercise 3.1E.20

Solve for r

  1. when d=180 and t=4.5
  2. in general
Answer
  1. r=40
  2. r=dt

In the following exercises, use the formula A=12bh

Exercise 3.1E.21

Solve for b

  1. when A=126 and h=18
  2. in general
Exercise 3.1E.22

Solve for h

  1. when A=176 and b=22
  2. in general
Answer
  1. h=16
  2. h=2Ab
Exercise 3.1E.23

Solve for h

  1. when A=375 and b=25
  2. in general
Exercise 3.1E.24

Solve for b

  1. when A=65 and h=13
  2. in general
Answer
  1. b=10
  2. b=2Ah

In the following exercises, use the formula I=Prt.

Exercise 3.1E.25

Solve for the principal, P for

  1. I=$5,480, r=4%, t=7 years
  2. in general
Exercise 3.1E.26

Solve for the principal, P for

  1. I=$3,950, r=6%, t=5 years
  2. in general
Answer
  1. P=$13,166.67
  2. P=Irt
Exercise 3.1E.27

Solve for the time, t for

  1. I=$2,376, P=$9,000, r=4.4%
  2. in general
Exercise 3.1E.28

Solve for the time, t for

  1. I=$624, P=$6,000, r=5.2%
  2. in general
Answer
  1. t=2 years
  2. t=IPr

In the following exercises, solve.

Exercise 3.1E.29

Solve the formula 2x+3y=12 for y

  1. when x=3
  2. in general
Exercise 3.1E.30

Solve the formula 5x+2y=10 for y

  1. when x=4
  2. in general
Answer
  1. y=5
  2. y=105x2
Exercise 3.1E.31

Solve the formula 3xy=7 for y

  1. when x=2
  2. in general
Exercise 3.1E.32

Solve the formula 4x+y=5 for y

  1. when x=3
  2. in general
Answer
  1. y=17
  2. y=54x
Exercise 3.1E.33

Solve a+b=90 for b.

Exercise 3.1E.34

Solve a+b=90 for a

Answer

a=90b

Exercise 3.1E.35

Solve 180=a+b+c for a

Exercise 3.1E.36

Solve 180=a+b+c for c

Answer

c=180ab

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=139x

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=113x2

Exercise 3.1E.43

Solve the formula xy=4 for y

Exercise 3.1E.44

Solve the formula xy=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=P2L2

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(F32) 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

10C

Writing Exercises

Exercise 3.1E.53

Solve the equation 2x+3y=6 for y

  1. when x=3
  2. in general
  3. Which solution is easier for you, 1 or 2? Why?
Exercise 3.1E.54

Solve the equation 5x2y=10 for x

  1. when y=10
  2. in general
  3. 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.

This is a table that has three rows and four columns. In the first row, which is a header row, the cells read from left to right: “I can…,” “confidently,” “with some help,” and “no-I don’t get it!” The first column below “I can…” reads “use the distance, rate, and time formula,” and “solve a formula for a specific variable.” The rest of the cells are blank.

ⓑ What does this checklist tell you about your mastery of this section? What steps will you take to improve?


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