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pogonyaev
2 years ago
5

how do i get the right hour when she runs 26. mile marathon at an average pace of 6.2 per mile. how long will take her to finish

the marathon ?round answer to the nearest minute . but it has to be the hours and minutes.
Mathematics
1 answer:
iris [78.8K]2 years ago
6 0

well, we know her rate is on average 6.2 miles per 1hr or 6.2 m/h, so how long will it be for 26 miles?

\begin{array}{ccll} miles&hrs\\ \cline{1-2} 6.2&1\\ 26&x \end{array}\implies \cfrac{6.2}{26}=\cfrac{1}{x}\implies 6.2x=26\implies x = \cfrac{26}{6.2}\implies x \approx 4.19355 \\\\\\ \textit{approximately~~~~ 4hrs 11mins and 37secs}

how did we get the minutes and seconds?  use the same rule or proportions above with hours and minutes,  4.19355, 4 + 0.19355, we know there are 60 mins per 1hr, how many in 0.19355 hrs? well, simply 60 * 19355, which gives us 11 minutes, and you can do the same thing for the seconds.

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3 years ago
The sum of two numbers is 86, and their difference is 20. Find the two numbers
sp2606 [1]

Answer:

x = 53, y = 33

Step-by-step explanation:

Let one of the numbers = x, & the other = y. Set the equations:

x + y = 86

x - y = 20

This is a system of equation, in which the variables must be true for both of them.

First, choose a equation to use. In this case, I will choose x + y = 86. Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Subtract y from both sides.

x + y = 86

x + y (-y) = 86 (-y)

x = 86 - y

Now, note the other equation: x - y = 20. You now know that x = 86 - y. Plug in 86 - y for x in the "other" equation:

x - y = 20

(86 - y) - y = 20

Simplify. Combine like terms:

86 - y - y = 20

86 - 2y = 20

Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS (Parenthesis, Exponents (& Roots), Multiplication, Division, Addition, Subtraction):

First, subtract 86 from both sides:

86 (-86) - 2y = 20 (-86)

-2y = 20 - 86

-2y = -66

Isolate the variable, y. Divide -2 from both sides:

(-2y)/-2 = (-66)/-2

<em>Note: Before we go any further, I want to remind you of division & multiplication rules. There are 3 kinds, when you are multiplying two positive numbers (+/+), when you are multiplying a positive number with a negative number (+/-), and when you are multiplying a two negative numbers (-/-)</em>. <em>Note the "table" in the bottom</em>:

________________________________________________________

(+/+) : Two positive numbers multiplied/divided with each other will always result in a positive answer:

Examples:

10/5 = 2

20/10 = 2

(+/-) : One positive number and one negative number multiplied/divided with each other will always result in a negative answer:

Examples:

20 x -5 = -100

50 x -3 = -150

(-/-) : Two negative numbers multiplied/divided with each other will always result in a positive answer:

Examples:

-30 x -5 = 150

-200/-10 = 20

________________________________________________________

Now, solve the equation:

(-2y)/-2 = (-66)/-2

y = -66/-2

Divide.

y = 33

One of your numbers (y) is 33. Plug in 33 for y in one of the equations:

x + y = 86

x + (33) = 86

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Subtract 33 from both sides.

x + 33 (-33) = 86 (-33)

x = 86 - 33

x = 53

Your answers: x = 53, y = 33.

Check: Plug in 53 for x, 33 for y in the equations:

<u>x + y = 86:</u>

(53) + (33) = 86

86 = 86 (True)

<u>x - y = 20</u>:

(53) - (33) = 20

20 = 20 (True)

Your answers: x = 53, y = 33

~

<u />

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