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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

4x+7y=29,x+3y=11 substitute method of linear equation
Srinu Reply
substitute method of linear equation
Srinu
Solve one equation for one variable. Using the 2nd equation, x=11-3y. Substitute that for x in first equation. this will find y. then use the value for y to find the value for x.
bruce
I want to learn
Elizebeth
help
Elizebeth
I want to learn. Please teach me?
Wayne
1) Use any equation, and solve for any of the variables. Since the coefficient of x (the number in front of the x) in the second equation is 1 (it actually isn't shown, but 1 * x = x), use that equation. Subtract 3y from both sides (this isolates the x on the left side of the equal sign).
bruce
2) This results in x=11-3y. x is note in terms of y. Use that as the value of x and substitute for all x in the first equation. The first equation becomes 4(11-3y)+7y =29. Note that the only variable left in the first equation is the y. If you have multiple variable, then something is wrong.
bruce
3) Distribute (multiply) the 4 across 11-3y to get 44-12y. Add this to the 7y. So, the equation is now 44-5y=29.
bruce
4) Solve 44-5y=29 for y. Isolate the y by subtracting 44 from birth sides, resulting in -5y=-15. Now, divide birth sides by -5 (since you have -5y). This results in y=3. You now have the value of one variable.
bruce
5) The last step is to take the value of y from Step 4) and substitute into the 2nd equation. Therefore: x+3y=11 becomes x+3(3)=11. Then multiplying, x+9=11. Finally, solve for x by subtracting 9 from both sides. Therefore, x=2.
bruce
6) The ordered pair of (2, 3) is the proposed solution. To check, substitute those values into either equation. If the result is true, then the solution is correct. 4(2)+7(3)=8+21=29. TRUE! Finished.
bruce
At 1:30 Marlon left his house to go to the beach, a distance of 5.625 miles. He rose his skateboard until 2:15, and then walked the rest of the way. He arrived at the beach at 3:00. Marlon's speed on his skateboard is 1.5 times his walking speed. Find his speed when skateboarding and when walking.
Andrew Reply
divide 3x⁴-4x³-3x-1 by x-3
Ritik Reply
how to multiply the monomial
Ceny Reply
Two sisters like to compete on their bike rides. Tamara can go 4 mph faster than her sister, Samantha. If it takes Samantha 1 hours longer than Tamara to go 80 miles, how fast can Samantha ride her bike? Got questions? Get instant answers now!
Seera Reply
how do u solve that question
Seera
Two sisters like to compete on their bike rides. Tamara can go 4 mph faster than her sister, Samantha. If it takes Samantha 1 hours longer than Tamara to go 80 miles, how fast can Samantha ride her bike?
Seera
Speed=distance ÷ time
Tremayne
x-3y =1; 3x-2y+4=0 graph
Juned Reply
Brandon has a cup of quarters and dimes with a total of 5.55$. The number of quarters is five less than three times the number of dimes
ashley Reply
app is wrong how can 350 be divisible by 3.
Raheem Reply
June needs 48 gallons of punch for a party and has two different coolers to carry it in. The bigger cooler is five times as large as the smaller cooler. How many gallons can each cooler hold?
Susanna Reply
Susanna if the first cooler holds five times the gallons then the other cooler. The big cooler holda 40 gallons and the 2nd will hold 8 gallons is that correct?
Georgie
@Susanna that person is correct if you divide 40 by 8 you can see it's 5 it's simple
Ashley
@Geogie my bad that was meant for u
Ashley
Hi everyone, I'm glad to be connected with you all. from France.
Lorris Reply
I'm getting "math processing error" on math problems. Anyone know why?
Ray Reply
Can you all help me I don't get any of this
Jade Reply
4^×=9
Alberto Reply
Did anyone else have trouble getting in quiz link for linear inequalities?
Sireka Reply
operation of trinomial
Justin 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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