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^{o}Fahrenheit. 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?