
2.6E: Exercises


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?

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?

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?

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?

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?

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?

75 mph

Solve a Formula for a Specific Variable

In the following exercises, use the formula $$d=rt$$.

Exercise $$\PageIndex{13}$$

Solve for $$t$$

1. when $$d=350$$ and $$r=70$$
2. in general

Exercise $$\PageIndex{14}$$

Solve for $$t$$

1. when $$d=240$$ and $$r=60$$
2. in general
1. $$t=4$$
2. $$t=\frac{d}{r}$$

Exercise $$\PageIndex{15}$$

Solve for $$t$$

1. when $$d=510$$ and $$r=60$$
2. in general

Exercise $$\PageIndex{16}$$

Solve for $$t$$

1. when $$d=175$$ and $$r=50$$
2. in general
1. $$t=3.5$$
2. $$t=\frac{d}{r}$$

Exercise $$\PageIndex{17}$$

Solve for $$r$$

1. when $$d=204$$ and $$t=3$$
2. in general

Exercise $$\PageIndex{18}$$

Solve for $$r$$

1. when $$d=420$$ and $$t=6$$
2. in general
1. $$r=70$$
2. $$r=\frac{d}{t}$$

Exercise $$\PageIndex{19}$$

Solve for $$r$$

1. when $$d=160$$ and $$t=2.5$$
2. in general

Exercise $$\PageIndex{20}$$

Solve for $$r$$

1. when $$d=180$$ and $$t=4.5$$
2. in general
1. $$r=40$$
2. $$r=\frac{d}{t}$$

In the following exercises, use the formula $$A=\frac{1}{2} b h$$

Exercise $$\PageIndex{21}$$

Solve for $$b$$

1. when $$A=126$$ and $$h=18$$
2. in general

Exercise $$\PageIndex{22}$$

Solve for $$h$$

1. when $$A=176$$ and $$b=22$$
2. in general
1. $$h=16$$
2. $$h=\frac{2 A}{b}$$

Exercise $$\PageIndex{23}$$

Solve for $$h$$

1. when $$A=375$$ and $$b=25$$
2. in general

Exercise $$\PageIndex{24}$$

Solve for $$b$$

1. when $$A=65$$ and $$h=13$$
2. in general
1. $$b=10$$
2. $$b=\frac{2 A}{h}$$

In the following exercises, use the formula $$I = Prt$$.

Exercise $$\PageIndex{25}$$

Solve for the principal, $$P$$ for

1. $$I=5,480$$, $$r=4\%$$, $$t=7$$ years
2. in general

Exercise $$\PageIndex{26}$$

Solve for the principal, $$P$$ for

1. $$I=3,950$$, $$r=6\%$$, $$t=5$$ years
2. in general
1. $$P=\ 13,166.67$$
2. $$P=\frac{I}{r t}$$

Exercise $$\PageIndex{27}$$

Solve for the time, $$t$$ for

1. $$I=2,376$$, $$P=9,000$$, $$r=4.4\%$$
2. in general

Exercise $$\PageIndex{28}$$

Solve for the time, $$t$$ for

1. $$I=624$$, $$P=6,000$$, $$r=5.2\%$$
2. in general
1. $$t=2$$ years
2. $$t=\frac{I}{Pr}$$

In the following exercises, solve.

Exercise $$\PageIndex{29}$$

Solve the formula $$2x+3y=12$$ for $$y$$

1. when $$x=3$$
2. in general

Exercise $$\PageIndex{30}$$

Solve the formula $$5x+2y=10$$ for $$y$$

1. when $$x=4$$
2. in general
1. $$y=−5$$
2. $$y=\frac{10-5 x}{2}$$

Exercise $$\PageIndex{31}$$

Solve the formula $$3x−y=7$$ for $$y$$

1. when $$x=−2$$
2. in general

Exercise $$\PageIndex{32}$$

Solve the formula $$4x+y=5$$ for $$y$$

1. when $$x=−3$$
2. in general
1. $$y=17$$
2. $$y=5−4x$$

Exercise $$\PageIndex{33}$$

Solve $$a+b=90$$ for $$b$$.

Exercise $$\PageIndex{34}$$

Solve $$a+b=90$$ for $$a$$

$$a=90-b$$

Exercise $$\PageIndex{35}$$

Solve $$180=a+b+c$$ for $$a$$

Exercise $$\PageIndex{36}$$

Solve $$180=a+b+c$$ for $$c$$

$$c=180-a-b$$

Exercise $$\PageIndex{37}$$

Solve the formula $$8 x+y=15$$ for $$y$$

Exercise $$\PageIndex{38}$$

Solve the formula $$9 x+y=13$$ for $$y$$

$$y=13-9 x$$

Exercise $$\PageIndex{39}$$

Solve the formula $$-4 x+y=-6$$ for $$y$$

Exercise $$\PageIndex{40}$$

Solve the formula $$-5 x+y=-1$$ for $$y$$

$$y=-1+5 x$$

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 $$y$$

$$y=\frac{11-3 x}{2}$$

Exercise $$\PageIndex{43}$$

Solve the formula $$x-y=-4$$ for $$y$$

Exercise $$\PageIndex{44}$$

Solve the formula $$x-y=-3$$ for $$y$$

$$y=3+x$$

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 $$W$$

$$W=\frac{P-2 L}{2}$$

Exercise $$\PageIndex{47}$$

Solve the formula $$C=\pi d$$ for $$d$$

Exercise $$\PageIndex{48}$$

Solve the formula $$C=\pi d$$ for $$\pi$$

$$\pi=\frac{C}{d}$$

Exercise $$\PageIndex{49}$$

Solve the formula $$V=L W H$$ for $$L$$

Exercise $$\PageIndex{50}$$

Solve the formula $$V=L W H$$ for $$H$$

$$H=\frac{V}{L W}$$

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.

$$10^{\circ} \mathrm{C}$$

Writing Exercises

Exercise $$\PageIndex{53}$$

Solve the equation $$2x+3y=6$$ for $$y$$

1. when $$x=−3$$
2. in general
3. Which solution is easier for you, 1 or 2? Why?

Exercise $$\PageIndex{54}$$

Solve the equation $$5x−2y=10$$ for $$x$$

1. when $$y=10$$
2. in general
3. Which solution is easier for you, 1 or 2? Why?