# 2.6E: Exercises

- Page ID
- 30110

## Practice Makes Perfect

**Use the Distance, Rate, and Time Formula**

In the following exercises, solve.

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

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

**Answer**-
290 miles

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

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

**Answer**-
30 miles

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?

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

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?

**Answer**-
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?

**Answer**-
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?

**Answer**-
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 \(d=240\) and \(r=60\)
- in general

**Answer**-
- \(t=4\)
- \(t=\frac{d}{r}\)

Solve for \(t\)

- when \(d=510\) and \(r=60\)
- in general

Solve for \(t\)

- when \(d=175\) and \(r=50\)
- in general

**Answer**-
- \(t=3.5\)
- \(t=\frac{d}{r}\)

Solve for \(r\)

- when \(d=204\) and \(t=3\)
- in general

Solve for \(r\)

- when \(d=420\) and \(t=6\)
- in general

**Answer**-
- \(r=70\)
- \(r=\frac{d}{t}\)

Solve for \(r\)

- when \(d=160\) and \(t=2.5\)
- in general

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 \(A=\frac{1}{2} b h\)

Solve for \(b\)

- when \(A=126\) and \(h=18\)
- in general

Solve for \(h\)

- when \(A=176\) and \(b=22\)
- in general

**Answer**-
- \(h=16\)
- \(h=\frac{2 A}{b}\)

Solve for \(h\)

- when \(A=375\) and \(b=25\)
- in general

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 \(I = Prt\).

Solve for the principal, \(P\) for

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

Solve for the principal, \(P\) for

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

**Answer**-
- \(P=\$ 13,166.67\)
- \( P=\frac{I}{r t}\)

Solve for the time, \(t\) for

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

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.

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

**Answer**-
- \(y=−5\)
- \(y=\frac{10-5 x}{2}\)

Solve the formula \(3x−y=7\) for \(y\)

- when \(x=−2\)
- in general

Solve the formula \(4x+y=5\) for \(y\)

- when \(x=−3\)
- in general

**Answer**-
- \(y=17\)
- \(y=5−4x\)

Solve \(a+b=90\) for \(b\).

Solve \(a+b=90\) for \(a\)

**Answer**-
\(a=90-b\)

Solve \(180=a+b+c\) for \(a\)

Solve \(180=a+b+c\) for \(c\)

**Answer**-
\(c=180-a-b\)

Solve the formula \(8 x+y=15\) for \(y\)

Solve the formula \(9 x+y=13\) for \(y\)

**Answer**-
\(y=13-9 x\)

Solve the formula \(-4 x+y=-6\) for \(y\)

Solve the formula \(-5 x+y=-1\) for \(y\)

**Answer**-
\(y=-1+5 x\)

Solve the formula \(4 x+3 y=7\) for \(y\)

Solve the formula \(3 x+2 y=11\) for \(y\)

**Answer**-
\(y=\frac{11-3 x}{2}\)

Solve the formula \(x-y=-4\) for \(y\)

Solve the formula \(x-y=-3\) for \(y\)

**Answer**-
\(y=3+x\)

Solve the formula \(P=2 L+2 W\) for \(L\)

Solve the formula \(P=2 L+2 W\) for \(W\)

**Answer**-
\(W=\frac{P-2 L}{2}\)

Solve the formula \(C=\pi d\) for \(d\)

Solve the formula \(C=\pi d\) for \(\pi\)

**Answer**-
\(\pi=\frac{C}{d}\)

Solve the formula \(V=L W H\) for \(L\)

Solve the formula \(V=L W H\) for \(H\)

**Answer**-
\(H=\frac{V}{L W}\)

## Everyday Math

**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.

**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

Solve the equation \(2x+3y=6\) for \(y\)

- when \(x=−3\)
- in general
- Which solution is easier for you, 1 or 2? Why?

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?