3.1E: Exercises

Last updated
Save as PDF

Page ID: 30484

$ \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } $ $ \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} $$\newcommand{\id}{\mathrm{id}}$ $ \newcommand{\Span}{\mathrm{span}}$ $ \newcommand{\kernel}{\mathrm{null}\,}$ $ \newcommand{\range}{\mathrm{range}\,}$ $ \newcommand{\RealPart}{\mathrm{Re}}$ $ \newcommand{\ImaginaryPart}{\mathrm{Im}}$ $ \newcommand{\Argument}{\mathrm{Arg}}$ $ \newcommand{\norm}[1]{\| #1 \|}$ $ \newcommand{\inner}[2]{\langle #1, #2 \rangle}$ $ \newcommand{\Span}{\mathrm{span}}$ $\newcommand{\id}{\mathrm{id}}$ $ \newcommand{\Span}{\mathrm{span}}$ $ \newcommand{\kernel}{\mathrm{null}\,}$ $ \newcommand{\range}{\mathrm{range}\,}$ $ \newcommand{\RealPart}{\mathrm{Re}}$ $ \newcommand{\ImaginaryPart}{\mathrm{Im}}$ $ \newcommand{\Argument}{\mathrm{Arg}}$ $ \newcommand{\norm}[1]{\| #1 \|}$ $ \newcommand{\inner}[2]{\langle #1, #2 \rangle}$ $ \newcommand{\Span}{\mathrm{span}}$$\newcommand{\AA}{\unicode[.8,0]{x212B}}$

Practice Makes Perfect

Use the Distance, Rate, and Time Formula

In the following exercises, solve.

Exercise $\PageIndex{1}$

Steve drove for 8$\frac{1}{2}$ hours at 72 miles per hour. How much distance did he travel?

Exercise $\PageIndex{2}$

Socorro drove for 4$\frac{5}{6}$ hours at 60 miles per hour. How much distance did she travel?

Answer: 290 miles

Exercise $\PageIndex{3}$

Yuki walked for 1$\frac{3}{4}$ hours at 4 miles per hour. How far did she walk?

Exercise $\PageIndex{4}$

Francie rode her bike for 2$\frac{1}{2}$ hours at 12 miles per hour. How far did she ride?

Answer: 30 miles

Exercise $\PageIndex{5}$

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 $\PageIndex{6}$

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 $\PageIndex{7}$

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 $\PageIndex{8}$

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 $\PageIndex{9}$

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 $\PageIndex{10}$

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 $\PageIndex{11}$

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 $\PageIndex{12}$

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 $\PageIndex{13}$

Solve for $t$

when $d=350$ and $r=70$
in general

Exercise $\PageIndex{14}$

Solve for $t$

when $d=240$ and $r=60$
in general

Answer

$t=4$
$t=\frac{d}{r}$

Exercise $\PageIndex{15}$

Solve for $t$

when $d=510$ and $r=60$
in general

Exercise $\PageIndex{16}$

Solve for $t$

when $d=175$ and $r=50$
in general

Answer

$t=3.5$
$t=\frac{d}{r}$

Exercise $\PageIndex{17}$

Solve for $r$

when $d=204$ and $t=3$
in general

Exercise $\PageIndex{18}$

Solve for $r$

when $d=420$ and $t=6$
in general

Answer

$r=70$
$r=\frac{d}{t}$

Exercise $\PageIndex{19}$

Solve for $r$

when $d=160$ and $t=2.5$
in general

Exercise $\PageIndex{20}$

Solve for $r$

when $d=180$ and $t=4.5$
in general

Answer

$r=40$
$r=\frac{d}{t}$

In the following exercises, use the formula $A=\frac{1}{2} b h$

Exercise $\PageIndex{21}$

Solve for $b$

when $A=126$ and $h=18$
in general

Exercise $\PageIndex{22}$

Solve for $h$

when $A=176$ and $b=22$
in general

Answer

$h=16$
$h=\frac{2 A}{b}$

Exercise $\PageIndex{23}$

Solve for $h$

when $A=375$ and $b=25$
in general

Exercise $\PageIndex{24}$

Solve for $b$

when $A=65$ and $h=13$
in general

Answer

$b=10$
$b=\frac{2 A}{h}$

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

Exercise $\PageIndex{25}$

Solve for the principal, $P$ for

$I=$5,480$, $r=4\%$, $t=7$ years
in general

Exercise $\PageIndex{26}$

Solve for the principal, $P$ for

$I=$3,950$, $r=6\%$, $t=5$ years
in general

Answer

$P=\$ 13,166.67$
$ P=\frac{I}{r t}$

Exercise $\PageIndex{27}$

Solve for the time, $t$ for

$I=$2,376$, $P=$9,000$, $r=4.4\%$
in general

Exercise $\PageIndex{28}$

Solve for the time, $t$ for

$I=$624$, $P=$6,000$, $r=5.2\%$
in general

Answer

$t=2$ years
$t=\frac{I}{Pr}$

In the following exercises, solve.

Exercise $\PageIndex{29}$

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

when $x=3$
in general

Exercise $\PageIndex{30}$

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

when $x=4$
in general

Answer

$y=−5$
$y=\frac{10-5 x}{2}$

Exercise $\PageIndex{31}$

Solve the formula $3x−y=7$ for $y$

when $x=−2$
in general

Exercise $\PageIndex{32}$

Solve the formula $4x+y=5$ for $y$

when $x=−3$
in general

Answer

$y=17$
$y=5−4x$

Exercise $\PageIndex{33}$

Solve $a+b=90$ for $b$.

Exercise $\PageIndex{34}$

Solve $a+b=90$ for $a$

Answer: $a=90-b$

Exercise $\PageIndex{35}$

Solve $180=a+b+c$ for $a$

Exercise $\PageIndex{36}$

Solve $180=a+b+c$ for $c$

Answer: $c=180-a-b$

Exercise $\PageIndex{37}$

Solve the formula $8 x+y=15$ for $y$

Exercise $\PageIndex{38}$

Solve the formula $9 x+y=13$ for $y$

Answer: $y=13-9 x$

Exercise $\PageIndex{39}$

Solve the formula $-4 x+y=-6$ for $y$

Exercise $\PageIndex{40}$

Solve the formula $-5 x+y=-1$ for $y$

Answer: $y=-1+5 x$

Exercise $\PageIndex{41}$

Solve the formula $4 x+3 y=7$ for $y$

Exercise $\PageIndex{42}$

Solve the formula $3 x+2 y=11$ for $y$

Answer: $y=\frac{11-3 x}{2}$

Exercise $\PageIndex{43}$

Solve the formula $x-y=-4$ for $y$

Exercise $\PageIndex{44}$

Solve the formula $x-y=-3$ for $y$

Answer: $y=3+x$

Exercise $\PageIndex{45}$

Solve the formula $P=2 L+2 W$ for $L$

Exercise $\PageIndex{46}$

Solve the formula $P=2 L+2 W$ for $W$

Answer: $W=\frac{P-2 L}{2}$

Exercise $\PageIndex{47}$

Solve the formula $C=\pi d$ for $d$

Exercise $\PageIndex{48}$

Solve the formula $C=\pi d$ for $\pi$

Answer: $\pi=\frac{C}{d}$

Exercise $\PageIndex{49}$

Solve the formula $V=L W H$ for $L$

Exercise $\PageIndex{50}$

Solve the formula $V=L W H$ for $H$

Answer: $H=\frac{V}{L W}$

Everyday Math

Exercise $\PageIndex{51}$

Converting temperature While on a tour in Greece, Tatyana saw that the temperature was 40^o Celsius. Solve for F in the formula $C=\frac{5}{9}(F−32)$ to find the Fahrenheit temperature.

Exercise $\PageIndex{52}$

Converting temperature Yon was visiting the United States and he saw that the temperature in Seattle one day was 50^oFahrenheit. Solve for C in the formula $F=\frac{9}{5}C+32$ to find the Celsius temperature.

Answer: $10^{\circ} \mathrm{C}$

Writing Exercises

Exercise $\PageIndex{53}$

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

when $x=−3$
in general
Which solution is easier for you, 1 or 2? Why?

Exercise $\PageIndex{54}$

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.

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

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

Practice Makes Perfect

Exercise \(\PageIndex{1}\)

Exercise \(\PageIndex{2}\)

Exercise \(\PageIndex{3}\)

Exercise \(\PageIndex{4}\)

Exercise \(\PageIndex{5}\)

Exercise \(\PageIndex{6}\)

Exercise \(\PageIndex{7}\)

Exercise \(\PageIndex{8}\)

Exercise \(\PageIndex{9}\)

Exercise \(\PageIndex{10}\)

Exercise \(\PageIndex{11}\)

Exercise \(\PageIndex{12}\)

Exercise \(\PageIndex{13}\)

Exercise \(\PageIndex{14}\)

Exercise \(\PageIndex{15}\)

Exercise \(\PageIndex{16}\)

Exercise \(\PageIndex{17}\)

Exercise \(\PageIndex{18}\)

Exercise \(\PageIndex{19}\)

Exercise \(\PageIndex{20}\)

Exercise \(\PageIndex{21}\)

Exercise \(\PageIndex{22}\)

Exercise \(\PageIndex{23}\)

Exercise \(\PageIndex{24}\)

Exercise \(\PageIndex{25}\)

Exercise \(\PageIndex{26}\)

Exercise \(\PageIndex{27}\)

Exercise \(\PageIndex{28}\)

Exercise \(\PageIndex{29}\)

Exercise \(\PageIndex{30}\)

Exercise \(\PageIndex{31}\)

Exercise \(\PageIndex{32}\)

Exercise \(\PageIndex{33}\)

Exercise \(\PageIndex{34}\)

Exercise \(\PageIndex{35}\)

Exercise \(\PageIndex{36}\)

Exercise \(\PageIndex{37}\)

Exercise \(\PageIndex{38}\)

Exercise \(\PageIndex{39}\)

Exercise \(\PageIndex{40}\)

Exercise \(\PageIndex{41}\)

Exercise \(\PageIndex{42}\)

Exercise \(\PageIndex{43}\)

Exercise \(\PageIndex{44}\)

Exercise \(\PageIndex{45}\)

Exercise \(\PageIndex{46}\)

Exercise \(\PageIndex{47}\)

Exercise \(\PageIndex{48}\)

Exercise \(\PageIndex{49}\)

Exercise \(\PageIndex{50}\)

Everyday Math

Exercise \(\PageIndex{51}\)

Exercise \(\PageIndex{52}\)

Writing Exercises

Exercise \(\PageIndex{53}\)

Exercise \(\PageIndex{54}\)

Self Check