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Proportions - Cooking

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Proportions and Baking Time

If an 2 pound item takes 90 minutes to cook at 350 degrees. how long do you cook it at 300 degrees?

Comments for Proportions - Cooking

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Mar 17, 2013
Baking Time
by: Staff


Answer

Part I


Mathematically, a proportion means that the relationship between variables is a constant.

The two variables for this problem are: temperature and time


There are several different types of proportions.


Direct Proportion

An increase in one variable corresponds to an increase in the other variable.

Given the variables "x" and "y":

y : x = k, a constant value

y = kx



Inverse Proportion (also called an indirect proportion)

An increase in one variable corresponds to a decrease the other variable.

Given the variables "x" and "y":

y * x = k, a constant value

y = k/x



Compound Proportion

A proportion which involves more than two variables.

Given the variables "x", "y", and "z":

z = k * y * x

k, a constant value

k = z / ( x * y)



Continued Proportion

An ordered set of numbers with the following characteristic: the ratio between every two successive terms is the same.

For example, 1:2:4:8:16

k = 2 = 2/1 = 4/2 = 8/4 . . .



Exponential proportion

y is directly proportional to an exponential function of x

Given the variables "x", and "y":

y = k * ax

both k and a are constant values



logarithmic proportion

Given the variables "x", and "y":

y = k * loga(x)

both k and a are constant values



To solve this problem, we assume that the lower the temperature, the longer the cooking time.

According to Newton's Law of Heating and Cooling, the rate of heating is proportional to the temperature difference between an object being cooked and the temperature of the oven.

This is a logarithmic proportion


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Mar 17, 2013
Baking Time
by: Staff


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Part II


The equation is:

formula for Newton's Law of Heating





t = the cooking time

T0 = initial temperature of the food (I will assume to be 75°)

Toven = temperature of the oven

Tfood = final temperature of the food (I will assume to be 200°)



when the oven temperature is 350° the cooking time is 90 minutes

Calculate constant for Newton's Law of Heating




Calculate cooking time when oven temperature is 300 degrees





The final answer is:

Math - final answer - cooking temperature when oven is 300 degrees








Thanks for writing.

Staff
www.solving-math-problems.com


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