Question

3

time (minutes)	15	30	45	60

a) what is the number of calories at 24 minutes?
b) what is the time at 280 calories?
4 consider the graph of the set of equivalent ratios shown.
a) determine the height in feet after 4 minutes. explain your reasoning.
b) determine the time when the height is 48 feet. explain your reasoning.
stretch optional
1 create a scenario to represent the relationship on the given graph. describe the quantities, label the axes, and identify at least 4 equivalent ratios.

Explanation:

Part 3 (a)

Step1: Find the rate of calories per minute

From the table, when time \( t = 15 \) minutes, calories \( c = 80 \). The rate \( r=\frac{80}{15}=\frac{16}{3}\) calories per minute.

Step2: Calculate calories at 24 minutes

Using the formula \( c = r\times t \), substitute \( r = \frac{16}{3} \) and \( t = 24 \). So \( c=\frac{16}{3}\times24 = 16\times8 = 128 \).

Step1: Find the rate of calories per minute (same as before, \( r=\frac{16}{3} \) calories per minute)

Step2: Calculate time for 280 calories

Using the formula \( t=\frac{c}{r} \), substitute \( c = 280 \) and \( r=\frac{16}{3} \). So \( t = 280\div\frac{16}{3}=280\times\frac{3}{16}=\frac{840}{16}=52.5 \) minutes.

Step1: Find the rate of height per minute

From the graph, when time \( t = 10 \) minutes, height \( h = 60 \) feet. Rate \( r=\frac{60}{10}=6 \) feet per minute.

Step2: Calculate height at 4 minutes

Using \( h = r\times t \), substitute \( r = 6 \) and \( t = 4 \). So \( h = 6\times4 = 24 \) feet.

Answer:

128

Part 3 (b)