QuestionEsther paints 7 faces in 21 minutes. Find the equation relating $f$ , the number of faces, and $m$ , the time in minutes.

Studdy Solution

STEP 1

Assumptions1. Esther paints7 faces every21 minutes. . The time taken to paint each face is the same.
3. We are asked to relate $f$ , the number of faces she paints, and $m$ , the time she spends painting in minutes.

STEP 2

First, we need to find the rate at which Esther paints faces. We can do this by dividing the number of faces she paints by the time she spends painting.
$Rate = \frac{Number\, of\, faces}{Time\, in\, minutes}$

STEP 3

Now, plug in the given values for the number of faces and time in minutes to calculate the rate.
$Rate = \frac{7\, faces}{21\, minutes}$

STEP 4

Calculate the rate at which Esther paints faces.
$Rate = \frac{7\, faces}{21\, minutes} = \frac{1\, face}{3\, minutes}$

STEP 5

Now that we have the rate, we can write an equation that relates $f$ , the number of faces she paints, and $m$ , the time she spends painting in minutes. The rate tells us that for every3 minutes,1 face is painted. So, for $m$ minutes, $f$ faces will be painted.
$f = \frac{m}{3}$ Esther paints $f$ faces in $m$ minutes.

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