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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?

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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

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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?

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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

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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?

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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

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Solve a Formula for a Specific Variable

In the following exercises, use the formula d = r t .

Solve for t
when d = 350 and r = 70
in general

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Solve for t
when d = 240 and r = 60
in general

t = 4 t = d r

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Solve for t
when d = 510 and r = 60
in general

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Solve for t
when d = 175 and r = 50
in general

t = 3.5 t = d r

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Solve for r
when d = 204 and t = 3
in general

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Solve for r
when d = 420 and t = 6
in general

r = 70 r = d t

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Solve for r
when d = 160 and t = 2.5
in general

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Solve for r
when d = 180 and t = 4.5
in general

r = 40 r = d t

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In the following exercises, use the formula A = 1 2 b h .

Solve for b
when A = 126 and h = 18
in general

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Solve for h
when A = 176 and b = 22
in general

h = 16 h = 2 A b

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Solve for h
when A = 375 and b = 25
in general

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Solve for b
when A = 65 and h = 13
in general

b = 10 b = 2 A h

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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

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Solve for the principal, P for
I = $ 3,950 , r = 6 % ,
t = 5 years
in general

P = $ 13 , 166.67 P = I r t

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Solve for the time, t for
I = $ 2,376 , P = $ 9,000 ,
r = 4.4 %
in general

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Solve for the time, t for
I = $ 624 , P = $ 6,000 ,
r = 5.2 %
in general

t = 2 years t = I Pr

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In the following exercises, solve.

Solve the formula 2 x + 3 y = 12 for y
when x = 3
in general

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Solve the formula 5 x + 2 y = 10 for y
when x = 4
in general

y = −5 y = 10 5 x 2

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Solve the formula 3 x y = 7 for y
when x = −2
in general

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Solve the formula 4 x + y = 5 for y
when x = −3
in general

y = 17 y = 5 4 x

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Solve a + b = 90 for b .

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Solve a + b = 90 for a .

a = 90 b

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Solve 180 = a + b + c for a .

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Solve 180 = a + b + c for c .

c = 180 a b

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

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

y = 13 9 x

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Solve the formula −4 x + y = −6 for y.

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Solve the formula −5 x + y = −1 for y.

y = −1 + 5 x

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Solve the formula 4 x + 3 y = 7 for y .

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Solve the formula 3 x + 2 y = 11 for y .

y = 11 3 x 4

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Solve the formula x y = −4 for y .

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Solve the formula x y = −3 for y .

y = 3 + x

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Solve the formula P = 2 L + 2 W for L .

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Solve the formula P = 2 L + 2 W for W .

W = P 2 L 2

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Solve the formula C = π d for d .

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Solve the formula C = π d for π .

π = C d

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Solve the formula V = L W H for L .

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Solve the formula V = L W H for H .

H = V L W

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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 = 5 9 ( F 32 ) to find the Fahrenheit temperature.

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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 = 9 5 C + 32 to find the Celsius temperature.

10°C

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Writing exercises

Solve the equation 2 x + 3 y = 6 for y
when x = −3
in general
Which solution is easier for you, or ? Why?

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Solve the equation 5 x 2 y = 10 for x
when y = 10
in general
Which solution is easier for you, or ? Why?

Answers will vary.

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Self check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

This is a table that has three rows and four columns. In the first row, which is a header row, the cells read from left to right: “I can…,” “confidently,” “with some help,” and “no-I don’t get it!” The first column below “I can…” reads “use the distance, rate, and time formula,” and “solve a formula for a specific variable.” The rest of the cells are blank.

What does this checklist tell you about your mastery of this section? What steps will you take to improve?

Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
what is titration
John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
hello friend how are you
Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir Reply
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Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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