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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 veterinarian is enclosing a rectangular outdoor running area against his building for the dogs he cares for. He needs to maximize the area using 100 feet of fencing. The quadratic equation A=x(100−2x) gives the area, A , of the dog run for the length, x , of the building that will border the dog run. Find the length of the building that should border the dog run to give the maximum area, and then find the maximum area of the dog run.
Elizabeth Reply
ggfcc
Mike
Washing his dad’s car alone, eight year old Levi takes 2.5 hours. If his dad helps him, then it takes 1 hour. How long does it take the Levi’s dad to wash the car by himself?
Gagan Reply
1,75hrs
Mike
I'm going to guess. Divide Levi's time by 2. Then divide 1 hour by 2. 1.25 + 0.5 = 1.3?
John
Oops I mean 1.75
John
I'm guessing this because since I have divide 1 hour by 2, I have to do the same for the 2.5 hours it takes Levi by himself.
John
Drew burned 1,800 calories Friday playing 1 hour of basketball and canoeing for 2 hours. On Saturday, he spent 2 hours playing basketball and 3 hours canoeing and burned 3,200 calories. How many calories did he burn per hour when playing basketball?
Marie Reply
Brandon has a cup of quarters and dimes with a total value of $3.80. The number of quarters is four less than twice the number of dimes. How many quarters and how many dimes does Brandon have?
Kendra Reply
Tickets to a Broadway show cost $35 for adults and $15 for children. The total receipts for 1650 tickets at one performance were $47,150. How many adult and how many child tickets were sold?
dana Reply
825
Carol
Arnold invested $64,000, some at 5.5% interest and the rest at 9%. How much did he invest at each rate if he received $4,500 in interest in one year? How do I do this
Tanesia Reply
how to square
Fiona Reply
easiest way to find the square root of a large number?
Jackie
the accompanying figure shows known flow rates of hydrocarbons into and out of a network of pipes at an oil refinery set up a linear system whose solution provides the unknown flow rates (b) solve the system for the unknown flow rates (c) find the flow rates and directions of flow if x4=50and x6=0
Sabee Reply
What is observation
adeyemi Reply
I'm confused by the question. Can you describe or explain the math question it pertains to?
Melissa
there is no math to it because all you use is your vision or gaze to the sorrounding areas
Cesarp
Teegan likes to play golf. He has budgeted $60 next month for the driving range. It costs him $10.55 for a bucket of balls each time he goes. What is the maximum number of times he can go to the driving range next month?
Sunnyshay Reply
5 times max
Anton
Felecia left her home to visit her daughter, driving 45mph. Her husband waited for the dog sitter to arrive and left home 20 minutes, or 1/3 hour later. He drove 55mph to catch up to Felecia. How long before he reaches her?
Sophia Reply
35 min
Debra
Carmen wants to tile the floor of his house. He will need 1,000 square feet of tile. He will do most of the floor with a tile that costs $1.50 per square foot, but also wants to use an accent tile that costs $9.00 per square foot. How many square feet of each tile should he plan to use if he wants the overall cost to be $3 per square foot?
Parker Reply
what you wanna get
Cesar
800 sq. ft @ $1.50 & 200 sq. ft @ $9.00
Marco
Geneva treated her parents to dinner at their favorite restaurant. The bill was $74.25. Geneva wants to leave 16 % of the total - bill as a tip. How much should the tip be?
74.25 × .16 then get the total and that will be your tip
David
$74.25 x 0.16 = $11.88 total bill: $74.25 + $11.88 = $86.13
ericka
yes and tip 16% will be $11.88
David
what is the shorter way to do it
Cesar Reply
Priam has dimes and pennies in a cup holder in his car. The total value of the coins is $4.21. The number of dimes is three less than four times the number of pennies. How many dimes and how many pennies are in the cup?
Alexandra 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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