Question

The amount of time it takes to cook a turkey increases with the weight of the turkey. it is recommended that you cook a 10-lb turkey for 3 hours. An extra 12 minutes of cooking time is necessary for each traditional pound of turkey. Is the cooking time proportional to the weigh of the turkey

Answer 1

Answer-

Cooking time is direct proportional to the weigh of the turkey.

Solution-

Time taken to cook a 10 lb turkey is 3 hours. The amount of time it takes to cook a turkey increases with the weight of the turkey. For an extra one pound of turkey it takes 12 minutes more.  

Taking the independent variable turkey weight in x-axis and dependent variable time in y-axis, a plot can be produced.

As shown in the figure, the line obtained from the data is a straight line.

So, Weight and Time are in direct proportion.  

Otherwise we can also check the relationship by comparing the slopes.

So, the data points are,

(x,y) = (10,180), (11,192), (12,204), (13,216), (14,228)

In order to be on a line all slopes between the points must be same.

Calculating the slope between (10,180), (11,192)

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{2}} =\frac{192-180}{11-10}=12$

Calculating the slope between  (11,192), (12,204)

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{2}} =\frac{204-192}{12-11}=12$

As the slopes are same, so these three points are in a straight line. Hence, they are in a direct relationship.

Answer 2

Answer:
The weight of the turkey is related linearly to the time taken to cook it, however, they are not proportional to each other.

Explanation:
1- Direct proportional means that when the weight of the turkey increases, the time required to cook it increase with the same amount, and vice versa
2- Inverse proportional means that when the weight of the turkey increases, the time required to cook it decrease, and vice versa
2- No proportionality relation means that the two are not related to each other.

Now, for the given problem, we are given that:
i. 10lb turkey takes 3 hours to cook
ii. an additional 12 minutes is added for every extra 1lb of turkey

Therefore:
If we have 10lb turkey ......> time required = 3 hr
If we have 11lb turkey .......> time required = 3 hr + 12 min
If we have 12lb turkey .......> time required = 3 hr + 12 min + 12 min
If we have 13lb turkey .......> time required = 3 hr + 12 min + 12 min + 12 min
Noticing the pattern, we can find that:
time required to cook the turkey increases as the weight of the turkey increases but not at the same rate.
This means that when the weight of the turkey is doubled, the time increases, however, it is not doubled.
This means that the weight of the turkey is related linearly to the time taken to cook it, however, they are not proportional to each other.

Hope this helps :)