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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?
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?
11.25 hours
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?
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?
75 mph
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?
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?
75 mph
Solve a Formula for a Specific Variable
In the following exercises, use the formula $d=rt$ .
Solve for
$t$
ⓐ when
$d=350$ and
$r=70$
ⓑ in general
Solve for
$t$
ⓐ when
$d=240\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}r=60$
ⓑ in general
ⓐ $t=4$ ⓑ $t=\frac{d}{r}$
Solve for
$t$
ⓐ when
$d=510\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}r=60$
ⓑ in general
Solve for
$t$
ⓐ when
$d=175\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}r=50$
ⓑ in general
ⓐ $t=3.5$ ⓑ $t=\frac{d}{r}$
Solve for
$r$
ⓐ when
$d=204\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}t=3$
ⓑ in general
Solve for
$r$
ⓐ when
$d=420\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}t=6$
ⓑ in general
ⓐ $r=70$ ⓑ $r=\frac{d}{t}$
Solve for
$r$
ⓐ when
$d=160\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}t=2.5$
ⓑ in general
Solve for
$r$
ⓐ when
$d=180\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}t=4.5$
ⓑ in general
ⓐ $r=40$ ⓑ $r=\frac{d}{t}$
In the following exercises, use the formula $A=\frac{1}{2}bh$ .
Solve for
$b$
ⓐ when
$A=126\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}h=18$
ⓑ in general
Solve for
$h$
ⓐ when
$A=176\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}b=22$
ⓑ in general
ⓐ $h=16$ ⓑ $h=\frac{2A}{b}$
Solve for
$h$
ⓐ when
$A=375\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}b=25$
ⓑ in general
Solve for
$b$
ⓐ when
$A=65\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}h=13$
ⓑ in general
ⓐ $b=10$ ⓑ $b=\frac{2A}{h}$
In the following exercises, use the formula I = Prt .
Solve for the principal,
P for
ⓐ
$I=\text{\$}\mathrm{5,480},r=4\%,$
$t=7\phantom{\rule{0.2em}{0ex}}\text{years}\phantom{\rule{0.2em}{0ex}}$
ⓑ in general
Solve for the principal,
P for
ⓐ
$I=\text{\$}\mathrm{3,950},r=6\%,$
$t=5\phantom{\rule{0.2em}{0ex}}\text{years}\phantom{\rule{0.2em}{0ex}}$
ⓑ in general
ⓐ $P=\text{\$}13,166.67$ ⓑ $P=\frac{I}{rt}$
Solve for the time,
t for
ⓐ
$I=\text{\$}\mathrm{2,376},P=\text{\$}\mathrm{9,000},$
$r=4.4\%$
ⓑ in general
Solve for the time,
t for
ⓐ
$I=\text{\$}624,P=\text{\$}\mathrm{6,000},$
$r=5.2\%$
ⓑ in general
ⓐ $t=2$ years ⓑ $t=\frac{I}{\mathrm{Pr}}$
In the following exercises, solve.
Solve the formula
$2x+3y=12$ for
y
ⓐ when
$x=3$
ⓑ in general
Solve the formula
$5x+2y=10$ for
y
ⓐ when
$x=4$
ⓑ in general
ⓐ $y=\mathrm{-5}$ ⓑ $y=\frac{10-5x}{2}$
Solve the formula
$3x-y=7$ for
y
ⓐ when
$x=\mathrm{-2}$
ⓑ in general
Solve the formula
$4x+y=5$ for
y
ⓐ when
$x=\mathrm{-3}$
ⓑ in general
ⓐ $y=17$ ⓑ $y=5-4x$
Solve $a+b=90$ for $b$ .
Solve $180=a+b+c$ for $a$ .
Solve the formula $8x+y=15$ for y.
Solve the formula $\mathrm{-4}x+y=\mathrm{-6}$ for y.
Solve the formula $\mathrm{-5}x+y=\mathrm{-1}$ for y.
$y=\mathrm{-1}+5x$
Solve the formula $4x+3y=7$ for y .
Solve the formula $x-y=\mathrm{-4}$ for y .
Solve the formula $P=2L+2W$ for $L$ .
Solve the formula $C=\pi d$ for $d$ .
Solve the formula $V=LWH$ for $L$ .
Converting temperature While on a tour in Greece, Tatyana saw that the temperature was 40 ^{o} Celsius. Solve for F in the formula $C=\frac{5}{9}\left(F-32\right)$ to find the Fahrenheit temperature.
Converting temperature Yon was visiting the United States and he saw that the temperature in Seattle one day was 50 ^{o} Fahrenheit. Solve for C in the formula $F=\frac{9}{5}C+32$ to find the Celsius temperature.
10°C
Solve the equation
$2x+3y=6$ for
$y$
ⓐ when
$x=\mathrm{-3}$
ⓑ in general
ⓒ Which solution is easier for you,
ⓐ or
ⓑ ? Why?
Solve the equation
$5x-2y=10$ for
$x$
ⓐ when
$y=10$
ⓑ in general
ⓒ Which solution is easier for you,
ⓐ or
ⓑ ? Why?
Answers will vary.
ⓐ 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?
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