QuestionMaria reads 40 pages in 2 hours. Find the equation for pages read vs. time, and explain each part of the equation.

Studdy Solution

STEP 1

Assumptions1. The relationship between the number of pages Maria reads and the time she spends reading is proportional. . Maria reads40 pages in two hours.

STEP 2

In a proportional relationship, the ratio of the two quantities is constant. We can write this relationship as an equation in the form y = kx, where y is the number of pages read, x is the time spent reading, and k is the constant of proportionality.

STEP 3

Given that Maria reads40 pages in two hours, we can find the constant of proportionality by dividing the number of pages read by the time spent reading.
$k = \frac{Number\, of\, pages\, read}{Time\, spent\, reading}$

STEP 4

Now, plug in the given values for the number of pages read and the time spent reading to calculate the constant of proportionality.
$k = \frac{40\, pages}{2\, hours}$

STEP 5

Calculate the constant of proportionality.
$k = \frac{40\, pages}{2\, hours} =20\, pages/hour$

STEP 6

Now that we have the constant of proportionality, we can write the equation for the relationship between the number of pages read (y) and the time spent reading (x).
$y = kx$

STEP 7

Plug in the value for the constant of proportionality into the equation.
$y =20x$ This equation represents the relationship between the number of pages Maria reads and the time she spends reading. The number of pages read (y) is equal to20 times the time spent reading (x). This means that for every hour Maria spends reading, she reads20 pages.

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QuestionMaria reads 40 pages in 2 hours. Find the equation for pages read vs. time, and explain each part of the equation.

Studdy Solution

STEP 1

Assumptions1. The relationship between the number of pages Maria reads and the time she spends reading is proportional. . Maria reads40 pages in two hours.

STEP 2

In a proportional relationship, the ratio of the two quantities is constant. We can write this relationship as an equation in the form y = kx, where y is the number of pages read, x is the time spent reading, and k is the constant of proportionality.

STEP 3

Given that Maria reads40 pages in two hours, we can find the constant of proportionality by dividing the number of pages read by the time spent reading.
$k = \frac{Number\, of\, pages\, read}{Time\, spent\, reading}$

STEP 4

Now, plug in the given values for the number of pages read and the time spent reading to calculate the constant of proportionality.
$k = \frac{40\, pages}{2\, hours}$

STEP 5

Calculate the constant of proportionality.
$k = \frac{40\, pages}{2\, hours} =20\, pages/hour$

STEP 6

Now that we have the constant of proportionality, we can write the equation for the relationship between the number of pages read (y) and the time spent reading (x).
$y = kx$

STEP 7

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QuestionMaria reads 40 pages in 2 hours. Find the equation for pages read vs. time, and explain each part of the equation.

Studdy Solution

STEP 1

Assumptions1. The relationship between the number of pages Maria reads and the time she spends reading is proportional. . Maria reads40 pages in two hours.

STEP 2

In a proportional relationship, the ratio of the two quantities is constant. We can write this relationship as an equation in the form y = kx, where y is the number of pages read, x is the time spent reading, and k is the constant of proportionality.

STEP 3

Given that Maria reads40 pages in two hours, we can find the constant of proportionality by dividing the number of pages read by the time spent reading.k=Number of pages readTime spent readingk = \frac{Number\, of\, pages\, read}{Time\, spent\, reading}k=TimespentreadingNumberofpagesread​

STEP 4

Now, plug in the given values for the number of pages read and the time spent reading to calculate the constant of proportionality.k=40 pages2 hoursk = \frac{40\, pages}{2\, hours}k=2hours40pages​

STEP 5

Calculate the constant of proportionality.k=40 pages2 hours=20 pages/hourk = \frac{40\, pages}{2\, hours} =20\, pages/hourk=2hours40pages​=20pages/hour

STEP 6

Now that we have the constant of proportionality, we can write the equation for the relationship between the number of pages read (y) and the time spent reading (x).y=kxy = kxy=kx

STEP 7

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Given that Maria reads40 pages in two hours, we can find the constant of proportionality by dividing the number of pages read by the time spent reading.
$k = \frac{Number\, of\, pages\, read}{Time\, spent\, reading}$

Now, plug in the given values for the number of pages read and the time spent reading to calculate the constant of proportionality.
$k = \frac{40\, pages}{2\, hours}$

Calculate the constant of proportionality.
$k = \frac{40\, pages}{2\, hours} =20\, pages/hour$

Now that we have the constant of proportionality, we can write the equation for the relationship between the number of pages read (y) and the time spent reading (x).
$y = kx$