Question

time (minutes)
① how many calories will courtesy burn if she hikes for 1 hour?
④ how many minutes would she have to hike to burn 240 calories
⑤ how many calories can she burn if she hikes for 105 minutes?

Explanation:

Part (c)

Step1: Determine the rate of calorie burn

From the graph, we can observe the pattern. Let's assume the relationship is linear. Looking at the points, when time \( x = 20 \) minutes, calories burned \( y = 120 \) (approx, from the graph). So the rate \( r=\frac{120}{20} = 6 \) calories per minute.

Step2: Calculate calories burned in 1 hour (60 minutes)

Using the rate, calories burned \( = 6\times60 = 360 \) calories.

Step1: Use the rate from part (c)

We know the rate is 6 calories per minute. Let \( t \) be the time in minutes. The formula is \( \text{Calories} = 6\times t \).

Step2: Solve for \( t \) when calories = 240

\( 240 = 6\times t \), so \( t=\frac{240}{6}=40 \) minutes.

Step1: Use the rate from part (c)

Rate is 6 calories per minute. Time is 105 minutes.

Step2: Calculate calories burned

Calories burned \( = 6\times105 = 630 \) calories.

Answer:

360 calories

Part (d)