Question

10 courtney burns 180 calories per 30 minutes of hiking.
(a) complete the table to chart her calorie expenditure for different amounts of time.
(b) plot the table of values on the graph.
(c) how many calories will courtney burn if she hikes for 1 hour?
(d) how many minutes would she have to hike to burn 240 calories?
(e) how many calories can she burn if she hikes for 105 minutes?

Explanation:

Part (a)

First, find the rate of calories burned per minute. Courtney burns 180 calories in 30 minutes, so the rate \( r=\frac{180}{30} = 6 \) calories per minute.

Step 1: For 10 minutes

Calories burned \( = 6\times10 = 60 \)

Step 2: For 5 minutes

Calories burned \( = 6\times5 = 30 \)

Step 3: For 20 minutes

Calories burned \( = 6\times20 = 120 \)

Step 4: For 75 minutes

Calories burned \( = 6\times75 = 450 \)

Step 5: For 45 minutes

Calories burned \( = 6\times45 = 270 \)

The completed table:

Time (minutes)	30	10	5	20	75	45

Part (c)

1 hour is 60 minutes. Using the rate of 6 calories per minute.

Step 1: Convert 1 hour to minutes

1 hour \( = 60 \) minutes

Step 2: Calculate calories burned

Calories burned \( = 6\times60 = 360 \)

We know the rate is 6 calories per minute. Let \( t \) be the time in minutes. We have \( 6t = 240 \)

Step 1: Solve for \( t \)

\( t=\frac{240}{6}=40 \)

Answer:

360

Part (d)