A car leaves a town traveling at 60 miles per hour. Two hours later, a second car leaves the town traveling the same route and overtakes the first car in 6 hours and 40 minutes. How fast was the second car traveling?

Answers

Answer 1

Answer:
After two hours, the first car has traveled (2 x 60) = 120 miles.
That's the gap that the second car has to close.

The second car closes the gap of 120 miles in 6-2/3 hours.
He must have exceeded the first car's speed by (120/6-2/3) mph.

6-2/3 = 20/3

120 divided by 20/3 = 120 x 3/20 = 360/20 = 18 mph

The second car exceeded the first car's speed by 18 mph,
so he had to be traveling (60 + 18) = 78 mph to catch up.

Check:

In 6-2/3 hours . . .

The first car covers (60 x 20/3) = 400 miles.

The second car covers (78 x 20/3) = 520 miles.
This is the same distance as the first car PLUS the 120
that he was behind when he started out.
yay !

Answer 2

Answer: 78 mph
The second car travels 520 miles in 400 minutes. 520/400=1.3. 1.3*60=78.

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Choose all the fractions that are equivalent to 4/12.1/3
9/27
5/15
2/8
8/24

Answers

The following fractions that are equivalent to 4/12: 1/3, 9/27, 5/15 and 8/24.

Equivalent Fraction

This classification refers to the fractions that represent the same value even if they are written with different numbers. For finding an equivalent fraction you should simplify the fraction until its simple form.

The given fraction is 4/12, when you divide the numerator and denominator by 4 you find 1/3 which represents the fraction in simplest form .

1/3 is equivalent to 4/12. Because the fraction in simplest form for 4/12 is 1/3 .

9/27 is equivalent to 4/12. Because the fraction in simplest form for 9/27 is 1/3 .

5/15 is equivalent to 4/12. Because the fraction in simplest form for 5/15 is 1/3 .

2/8 is not equivalent to 4/12. Because the fraction in simplest form for 2/8 is 1/4 .

8/24 is equivalent to 4/12. Because the fraction in simplest form for 8/24 is 1/3 .

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Answer:

1/3 ! 5/15 ! 8/24 ! 9/27

Step-by-step explanation:

i know math

A scientist has two solutions, which she has labeled Solution A 60% and Solution B 75% Each contains salt. She knows that Solution A is salt and Solution B is salt. She wants to obtain ounces of a mixture that is salt. How many ounces of each solution should she use

Answers

Answer:

The answer is "180".

Step-by-step explanation:

Please find the complete question in the attached file.

Let's

x = ounces solution of A

y = ounces solution of B

$x + y = 180 \n\ny = 180 - x\n\n0.60x + 0.85y = 0.75(180)\n\n0.60x + 0.85y = 135\n\n$

Multiply both sides of the equation by 100 to remove the decimal points.

$60x + 85y = 13500\n\n60x + 85(180 - x) = 13500\n\n60x + 15300 - 85x = 13500\n\n-25x = -1800\n\nx = 72\ \ ounces\n\ny = 180 - 72 \n\ny = 108 \ \ ounces\n\n$

Rick used 4-2-3 yards to sew 3-1-2 shirts what is the unit rate of cloth he used in terms of yards per shirt Mathematics 7th grade

Answers

If Rick used 4 2/3 yards of fabric to sew 3 1/2 shirts. The unit rate of cloth he used in terms of yards per shirt will be 4/3.

What is an arithmetic operation?

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

It is given that, Rick used 4 2/3 yards of fabric to sew 3 1/2 shirts.

We'll apply division by Splitting into equal halves or groups, the division may be used to decide how to distribute a dish of cookies evenly among a group.

The unit rate of cloth he used in terms of yards per shirt is found by dividing the 3 1/2 shirts by 4 2/3 yards,

$= 4 (2)/(3) / 3 (1)/(2) \n\n = (14)/(3) / (7)/(2) \n\n = (14)/(3) * (2)/(7) \n\n = (4)/(3)$

Thus, if Rick used 4 2/3 yards of fabric to sew 3 1/2 shirts. The unit rate of cloth he used in terms of yards per shirt will be 4/3.

The question is incomplete

The complete question is"Rick used 4 2/3 yards of fabric to sew 3 1/2 shirts. What is the unit rate of cloth he used in terms of yards per shirt?"

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To my knowledge, the answer should be there is no difference since I found the sum, however the answer is something else, could someone please explain

Answers

In the first series, the summation applies to the whole (2n+3) inside
the parentheses, so the 3 gets summed up 5 times.

But in the second one, the summation only applies to the 2n , so
the 3 is only added after the summation is finished.

The difference between five 3s the first time and one 3 the second time
is your 12 .

The difference between them is 12 because :
the sum of first series is : 2 * ( 1 + 2 + 3 + 4 + 5 ) + 15;
the sum of the second series is : 2 * ( 1 + 2 + 3 + 4 + 5 ) + 3.

Which inequality represents the values of X that insure triangle ABC exists

Answers

Answer:

7/4 < x < 11/2

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.

Please have a look at the attached photo.

My answer

Given the information:

AB: 2x + 4
BC: 6x
AC: 16

All of these three triangle inequalities must be satisfied:

AB +BC > AC

<=> 2x + 4 + 6x > 18

<=> 8x > 14

<=> x > 7/4

BC +CA > BA

6x + 18 > 2x + 4

<=> 4x > -14

<=> x > -14/4

CA +AB > CB

18 + 2x + 4 > 6x

<=> 22 > 4x

<=> x < 11/2

So the inequality represents the values of X that insure triangle ABC exists is: 7/4 < x < 11/2

Hope it will find you well.

Write an equation of the line in point-slope form through each pair of points (9,5) and (8,2) A) y+5=3(x+9)
B )y+5=1/3(x+9)
C) y-5=3(x-9)
D) y-5=1/3(x-9)

Answers

$\bf (\stackrel{x_1}{9}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{9}}}\implies \cfrac{-3}{-1}\implies 3 \n\n\n \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\n \cline{1-1} \n y-y_1=m(x-x_1) \n\n \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{3}(x-\stackrel{x_1}{9})$

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