Question

According to the graph:Part A: Which activity burns more calories per minute-kayaking or hiking.?Part B: How many total calories do you burn?

Answer 1

We are given that the number of calories

"y" burned after "x" minutes of kayaking are given by:

`y=4.5x`

This is an equation of the form:

`y=mx`

Where "m" is the slope. In this case, the slope represents the number of calories per minute that are burned by the activity, therefore, the number of calories per minute is:

`m_k=4.5(cal)/(\min )`

Now, to determine the number of calories per minute by Hiking we need to determine the slope of the given graph. To do that we will use the following formula:

`m=(y_2-y_1)/(x_2-x_1)`

Where:

`(x_1,y_1),(x_2,y_2)`

Are points on the graph. Therefore, we need to choose two points from the graph. we will use:

`\begin{gathered} (x_1,y_1)=(0,0) \\ (x_2,y_2)=(5,30) \end{gathered}`

Substituting the points in the formula for the slope we get:

`m=(30-0)/(5-0)=6`

Therefore, by Hiking we have:

`m_H=6(cal)/(\min )`

Therefore, more calories per minute are burned by Hiking.

Part B. Now we are given that each activity is performed for 45 minutes. For the number of calories burned by hiking we have the following equation:

`y=4.5x`

Now we substitute the value of "x = 45 min":

`\begin{gathered} y=4.5(45) \\ y=202.5 \end{gathered}`

Therefore, by Kayaking the number of calories burned is 202.5 cal.

Now, in the case of Hiking we already determined the slope to be 6. Since the graph show that the line passes through the origin, this means that the equation of the line is of the form:

`y=mx`

Substituting the value of the slope we get:

`y=6x`

Now we substitute the 45 min:

`\begin{gathered} y=6(45) \\ y=270 \end{gathered}`

Therefore, 270 cal are burned by Hiking. The total number of calories is then the sum of the calories burned by each activity:

`\text{Tcal}=202.5cal+270\text{cal}=472.5cal`

Therefore, the total number of calories burned is 472.5 calories.