Question

The label of an energy bar with a mass of $68g$lists the nutrition facts as $39g$of carbohydrate, $5g$of fat, and $10g$of protein. $(2.5,2.6,3.4,3.6)$

$\left(a\right)$Using the energy values for carbohydrates, fats, and proteins (see Table), what are the total kilocalories listed for the energy bar? (Round off answers for each food type to the tens place.)

$\left(b\right)$What are the kilojoules for the energy bar? (Round off answers for each food type to the tens place.)

$\left(c\right)$If you obtain $160kJ$, how many grams of the energy bar did you eat?

$\left(d\right)$If you are walking and using energy at a rate of $840kJ/h$, how many minutes will you need to walk to expend the energy from two energy bars?

Short answer

Part $\left(a\right)$

$\left(a\right)$The energy values are as,

Carbohydrates$=150kcal.$

proteins $=40kcal.$

fats $=45kcal.$

Part $\left(b\right)$

role="math" $\left(b\right)$The energy values in kilojoules as,

Carbohydrates$=660kJ.$

proteinsrole="math" localid="1651733910413" $=170kJ.$

fats$=190kJ.$

Part $\left(c\right)$

$\left(c\right)$The enegy bar mass of$160kJ$is$11g.$

Part $\left(d\right)$

$\left(d\right)$ Aa a result,a person would have to walks for $2.4hrs$ to absorb the power obtained from two black cherry nut bars.

Step-by-step solution

Step: 1 Given information: (Part a)  

Given are: $68g$mass energy bar label and $39g$of carbohydrates and $5g$of fats and $10g$of protein.

To find the kilocalories of given energy bar.

Step: 2 Finding energy: (part a) 

The price of power received for each grams is listed in the table below:

The quantity of energy in a black cherry walnut bar that comes from carbohydrates is computed as follows:

$39g\times \frac{4\mathrm{kcal}}{1\mathrm{g}}=150\mathrm{kcal}$

The energy in bar is $150\mathrm{kcal}.$

Step: 3 Fats and protein energy: (Part a)

The quantity of energy in a black cherry walnut bar that comes from fats is computed as follows:

$5g\times \frac{9\mathrm{kcal}}{1g}=45\mathrm{kcal}$

The quantity of energy in a black cherry walnut bar that comes from protein is computed as follows:

$10\mathrm{g}\times \frac{4\mathrm{kcal}}{1g}=40\mathrm{kcal}$

Step: 3 Given information: (Part b)  

Given are:$68g$of energy bar label mass and $39g$of carbohydrates and $5g$of fats and $10g$of protein.

To find the kilojoules of bar energy.

Step: 5 Energy calculation in kilojoules: (Part b) 

The quantity of energy in a black cherry walnut bar that comes from Carbohydrates is computed as follows:

$39\mathrm{g}\times \frac{17\mathrm{kJ}}{1g}=660\mathrm{kJ}$

The quantity of energy in a black cherry walnut bar that comes from fats is computed as follows:

$5\mathrm{g}\times \frac{38\mathrm{kJ}}{1g}=190\mathrm{kJ}$

The quantity of energy in a black cherry walnut bar that comes from protein is computed as follows:

$10\mathrm{g}\times \frac{17\mathrm{kJ}}{1g}=170\mathrm{kJ}$

Step: 6 Given information: (Part c)  

Given are: $68g$of energy bar label mass and $39g$of carbohydrates and $5g$of fats and $10g$of protein.

To find the how many grammes of the energy bar consume if $160kJ$.

Step: 7 Finding bar mass: (Part c) 

The amount of energy as

$660\mathrm{kJ}+190\mathrm{kJ}+170\mathrm{kJ}=1,020\mathrm{kJ}$

The bar mass as

$160\mathrm{kJ}\times \frac{68\mathrm{g}}{1,020\mathrm{kJ}}=11\mathrm{g}$

As a result,the bar mass as$11g.$

Step: 8 Given information: (Part d)  

Given are: $68g$of energy bar label mass and $39g$of carbohydrates and $5g$of fats and $10g$of protein.

To find the energy required to walk.

Step: 9 Finding energy: (Part d) 

The quantity of energy in a black cherry walnut bar is computed as follows:

$1,020\mathrm{kJ}+1,020\mathrm{kJ}=2,040\mathrm{kJ}$

The energy as

$2,040\mathrm{kJ}\times \frac{1\mathrm{h}}{840\mathrm{kJ}}=2.4\mathrm{h}$

Aa a result,a person would have to walks for$2.4hrs$ to absorb the power obtained from two black cherry nut bars.