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 40o 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 50oFahrenheit. 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.
ⓑ What does this checklist tell you about your mastery of this section? What steps will you take to improve?