# 3.1E: Exercises

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## 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^{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?