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2 years ago

Jose runs 3 mikes in 28 minutes. At the same rate, how many miles would he run in 42 minutes?

Mathematics

2 answers:

My name is Ann [436]2 years ago

8 0

Answer:

$4.5 \: miles$

Step-by-step explanation:

$3 \: miles \: in \: 28 \: minutes.$

$x \: miles \: in \: 42 \: minutes.$

$28x=42 \times 3$

$28x=126$

$\frac{28x}{28}=\frac{126}{28}$

$x=\frac{9}{2}$

asambeis [7]2 years ago

7 0

Answer:

$4.5 \: \: miles \\$

Step-by-step explanation:

$3 \: \: miles = 28 \: \: min \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: x \: \: \: = 42 \: min$

use cross multiplication

$42 \times 3 = 28 \times x \\ 12 6 = 28x \\ \frac{126}{28} = \frac{28x}{28} \\ x = 4.5 \: \: miles$

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Step-by-step explanation:

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Answer:

$x=\frac{12}{7} \\y=\frac{12}{5} \\z=-12$

Step-by-step explanation:

Let's re-write the equations in order to get the variables as separated in independent terms as possible \:

First equation:

$\frac{xy}{x+y} =1\\xy=x+y\\1=\frac{x+y}{xy} \\1=\frac{1}{y} +\frac{1}{x}$

Second equation:

$\frac{xz}{x+z} =2\\xz=2\,(x+z)\\\frac{1}{2} =\frac{x+z}{xz} \\\frac{1}{2} =\frac{1}{z} +\frac{1}{x}$

Third equation:

$\frac{yz}{y+z} =3\\yz=3\,(y+z)\\\frac{1}{3} =\frac{y+z}{yz} \\\frac{1}{3}=\frac{1}{z} +\frac{1}{y}$

Now let's subtract term by term the reduced equation 3 from the reduced equation 1 in order to eliminate the term that contains "y":

$1=\frac{1}{y} +\frac{1}{x} \\-\\\frac{1}{3} =\frac{1}{z} +\frac{1}{y}\\\frac{2}{3} =\frac{1}{x} -\frac{1}{z}$

Combine this last expression term by term with the reduced equation 2, and solve for "x" :

$\frac{2}{3} =\frac{1}{x} -\frac{1}{z} \\+\\\frac{1}{2} =\frac{1}{z} +\frac{1}{x} \\ \\\frac{7}{6} =\frac{2}{x}\\ \\x=\frac{12}{7}$

Now we use this value for "x" back in equation 1 to solve for "y":

$1=\frac{1}{y} +\frac{1}{x} \\1=\frac{1}{y} +\frac{7}{12}\\1-\frac{7}{12}=\frac{1}{y} \\ \\\frac{1}{y} =\frac{5}{12} \\y=\frac{12}{5}$

And finally we solve for the third unknown "z":

$\frac{1}{2} =\frac{1}{z} +\frac{1}{x} \\\\\frac{1}{2} =\frac{1}{z} +\frac{7}{12} \\\\\frac{1}{z} =\frac{1}{2}-\frac{7}{12} \\\\\frac{1}{z} =-\frac{1}{12}\\z=-12$

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2 years ago

Jose runs 3 mikes in 28 minutes. At the same rate, how many miles would he run in 42 minutes?​

Jose runs 3 mikes in 28 minutes. At the same rate, how many miles would he run in 42 minutes?